The speed of the arrow that has a mass of 88 g is 13.96 m/s
The mass of the arrow = 88 g
The force exerted by the string on the arrow = 110 N
The length of the arrow = 78 cm
The speed of the arrow can be found using the formula,
F = mv² / 2d
where F is the force exerted by the string on the arrow
m is the mass of the arrow
v is the speed of the arrow
d is the length of the arrow
Let us rearrange the equation,
v² = 2Fd / m
Let us substitute the known values in the above equation, we get
v² = 2 x110 x 78 x 10⁻² / 0.88
= 17160 x 10⁻² / 0.88
= 19500 x 10⁻²
= 195
v = √195
= 13.96 m/s
Therefore, the speed of the arrow = 13.96 m/s
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a person leaps from an airplane 5500 feet above the ground and deploys her/his parachute after 4 seconds. assume that the air resistance both before and after deployment of the parachute results in a deceleration proportional to the person's velocity, but with a different constant of proportionality. before deployment, take the constant to be 0.15 sec , and after deployment use the value 1.3 sec . (the acceleration due to gravity is 32.2ft/sec . note also that the constants of proportionality given are , not k.) how fast is the person going when the parachute is deployed? speed
The speed of the person when the parachute is deployed in ft/s is calculated to be 135.6 ft/s.
The forces influencing the mass m skydiver at any particular time are:
i) Fg = mg j
ii) FR = -k v
As demonstrated in the following diagram provided in the attachment, we have taken a reference with its origin at the point the movement starts and the positive y axis along the direction of the movement (vertically down).
Writing down Newton's equation, we have:
ΣFi = FR + Fg = m a
Considering that the movement occurs on the y-axis, dropping the vector notation and replacing it with the modular values of FR and Fg, with the signs in accordance with the elected reference frame, we have:
m a = m dv/dt = m g - k v ----(1)
Before the parachute is deployed, ρ₁ m = 0.15 s⁻¹. The velocity in this regime is labeled v₁.
After the parachute is deployed, ρ₂ m = 1.3 s⁻¹. The velocity in this regime is labeled v₂.
Let's solve equation (1) in the first regime. The following is the complete solution for the velocity as a function of time:
v(t) = v 1h(t) + v 1p(t)
This is the result of adding the homogeneous equation's solution to one specific in-homogeneous equation's solution. Given, k = ρ₁ m and arranging equation (1), we have:
dv₁/dt + ρ₁ v₁ = g
The homogeneous equation takes the following form:
dv₁/dt + ρ₁ v₁ = 0
The solution is then written:
v 1h = C e^(ρ₁ t), where C is an arbitrary constant.
The inhomogeneous equation has the following specific solution:
v 1p = g/ρ₁
This can be checked by direct substitution. Let's enforce the initial condition v₁(0) = 0 (the man starts the fall without initial velocity) to determine the constant C:
C = g/ρ₁ ⇒ v(t) = g/ρ₁ [1 - e^(ρ₁ t)]
The second initial condition is y(0) = 0 and is only necessary to determine the position as a function of time. Substituting, we get:
v₁ (7) = 135.6 ft/s
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why are they called projectile electrons and not just electrons? do we have another type of electrons?
Projectile electrons are called as such because they are electrons that are emitted from a sample and are used as a projectile to ionize other species in a mass spectrometer.
The term "projectile electrons" serves as a descriptor of their function and is used to differentiate them from other types of electrons in the mass spectrometer.
Yes, there are other types of electrons, such as bound electrons that are associated with atoms and molecules, free electrons that are not associated with any species, and photoelectrons, which are electrons that are emitted when a material absorbs light.
Projectile electrons are just one type of electron, used specifically in mass spectrometry for ionization purposes.
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In projectile motion, the ______ along the ____ is constant.
Answer:
In projectile motion, the velocity along the x-axis is constant.
Explanation:
In case of projectile motion the vertical component of particle's velocity changes continuously because of the force acting in vertical direction which is its own weight.
But in the horizontal direction as there is no force acting on the object; therefore its horizontal velocity remains constant.
when two resistors are in parallel, the current tends to pass from the: group of answer choices passes equally smaller resistor larger resistor cannot be determined
When the two resistors are in parallel, the current through the the larger resistor will be less and the current through the smaller resistor will be more.
According to ohm's law, the electric current is proportional to the voltage applied, so we can write,
V ∝ I
V = IR
R is the resistance.
In parallel, the voltage is same. So, we can write,
I ∝ 1/R
So, as we can see that the current and the resistance are inversely related, we can conclude that when the two resistors are connected in parallel, the current from the larger resistor will be less and current through the smaller resistor will be more.
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explain how each of galileo's telescopic discoveries contradicted the ptolemaic theory.
In the ancient world, the geocentric Ptolemaic theory served as the standard for cosmology. According to this theory, the Earth was at the centre of the cosmos and that every other celestial body rotated around it.
However, Galileo Galilei's telescopic findings made with his recently developed telescope presented multiple problems with this idea.
1. Venus' phases. Galileo noted that Venus cycled through phases resembling those of the Moon, which could only be true if Venus rotated around the Sun and not the Earth.
2. Galileo discovered that Jupiter has four moons that orbit the planet, which disproved the notion that all celestial bodies revolve around the Earth.
3. Galileo noticed that the Moon had mountains and craters, which called into question the notion that it was a perfect sphere that remained unchanged across time.
4. The Sunspots: Galileo discovered that the Sun's spots evolved through time, altering in size and shape, which cast doubt on the notion that the Sun was a perfect, immutable celestial body.
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A child's water pistol shoots a stream of water through a 1.0 mm diameter nozzle at a speed of 4.0 m/s. Squeezing the trigger pressurizes the water reservoir inside the pistol. It is reasonable to assume that the water in the reservoir is at rest. Assume that the water is an ideal fluid.1. What is the volume flow rate in mL/s as the trigger is being squeezed? (Express your answer in milliliters per second.)2. What is the gauge pressure inside the reservoir?
(1) 0.0314 ml/s is the volume flow rate in mL/s as the trigger is being squeezed. (2) 9800 psi is the gauge pressure inside the reservoir?
(1) The volume flow rate can be calculated using the equation for the continuity of a fluid, which states that the volume flow rate through any given section of a pipe is constant, provided that the velocity and cross-sectional area of the pipe remain constant.
=> Q = A x v
here Q is volume flow rate,
A is cross-sectional area of pipe,
v is velocity of the fluid.
The cross-sectional area of the nozzle is:-
=> A = π x (d/2)^2
here d is diameter of the nozzle.
Now, putting values, we have:-
=> A
= π x (1.0 mm / 2)^2
= 7.86 * 10^-8 m^2
=> Q
= A x v
= 7.86 x 10^-8 m^2 x 4.0 m/s
= 3.14 x 10^-7 m^3/s
To convert the volume flow rate to milliliters per second, we need to multiply by 1000 to convert from cubic meters to cubic centimeters, and then divide by 1000 to convert from cubic centimeters to milliliters:
=> Q
= 3.14 x 10^-7 m^3/s x 1000 cm^3/m^3 / 1000 ml/cm^3
= 0.0314 ml/s
Hence, volume flow rate = 0.0314 ml/s.
(2) The gauge pressure inside the reservoir can be calculated using the equation for the pressure at a point in a fluid at rest, which is given by:
=> P = ρgh
here P is pressure,
ρ is density of the fluid,
g is acceleration (gravity),
h is height of the fluid above the point of interest.
Since the water in the reservoir is at rest,
The gauge pressure is:-
=> P
= ρgh
= 1000 x 9.8 x h
= 9800h psi
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Write an analysis comparing pioneer forecasting and current forecasting.
While the Earth was defended from the rays of the summer sun, and protected from the cold blasts of winter by an impenetrable covering of fallen leaves, and a thick growth of forest trees, there can be no doubt of the winters being milder, and summers more temperate than at present. It was especially noticed in the summer nights, which were so cool as to render a blanket both a pleasant and desirable covering to the sleeper.The earth, when protected by the forest from the influence of cold winds, and covered with a thick coat of fallen leaves, never froze; while in an adjacent cleared field it froze to the depth of several inches. The warm vapor constantly rising from the earth, served to temper the atmosphere and render it more mild than at present….It is true there were some very cold winters and deep snows, but they were not so changeable as now: nevertheless it yet remains certain, that the winters are much more uniform, while a country is covered with forest, and not subject to such sudden changes of temperatures as they are in an open region…The summers are as much changed as the winters: fifty years since, they are more humid, and there was more generally that conditions of the atmosphere which we call sultry, and now experience in warm weather after a heavy rain. This constant humidity of the air was occasioned by the regular evaporation of moisture from the leaves of the trees, shrubs, and plants that clothed the face of the earth, and shut out the drying influence of the sun and air. The same causes kept the surface constantly moist, and afforded a regular supply of water to the springs, during the summer as well as the winter, protecting the tender roots of the grasses and other plants from the cold, caused them to vegetate early in the spring, and bring forth a plentiful supply of herbage for the wild animals of the forest, and domestic cattle of the new settler.
historical data as inputs, forecasting is a process that produces accurate predictions of the future course of trends.
What is Forecasting?Businesses use forecasting to decide how to spend their budgets and make plans for upcoming expenses. Typically, this is based on the anticipated demand for the offered goods and services.
To predict how trends, such as the GDP or unemployment, will change in the upcoming quarter or year, equity analysts use forecasting. Finally, statisticians can examine the probable effects of a change in business operations via forecasting.
Data may be gathered, for example, on how changing business hours affects consumer happiness or how changing particular work conditions affects staff productivity.
Therefore, historical data as inputs, forecasting is a process that produces accurate predictions of the future course of trends.
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For each statement below write “primary” or “secondary” to describe that type of data.
i. An astronomer uses data from a science book to develop an explanation about the atmospheres on different planets.
ii. A student uses a table from a magazine to find out about moons around the planets.
iii. A teacher use a telescope to observe the crafters on the moon.
Which data are likely to be more reliable?
Explain your answer.
Answer:
Explanation:
All three sources of data (the science book, the magazine, and the telescope) are likely to be reliable, but to varying degrees.
i. The science book is likely to be a reliable source of information about the atmospheres on different planets, as it is likely to have been written by experts in the field and reviewed by other experts before being published. However, the information may not be as up-to-date as newer research.
ii. The magazine table is likely to be a reliable source of information about moons around the planets, as it is likely to have been written by experts in the field and reviewed by other experts before being published. However, the information may not be as detailed or in-depth as information from a scientific journal.
iii. The telescope observation is likely to be the most reliable source of information about the craters on the moon, as it provides direct observation of the phenomenon in question. However, it is important to note that the accuracy of the observations may depend on the quality of the telescope and the skill of the observer.
In general, information from scientific journals and textbooks written by experts in the field is generally considered more reliable than information from popular sources such as magazines, newspapers, or websites. Direct observations made using scientific instruments are generally considered to be the most reliable sources of information.
A 3520 kg truck moving north at
16.0 m/s makes an INELASTIC
collision with an 1480 kg car
moving 21.0 m/s east. What is the
magnitude of their (joint) velocity
after the collision?
Answer:
26.4 m/s
Explanation:
In the case of 2D inelastic collision the algebraic approach gets very complicated so it is better to use
Geometrical (vector) approach
In elastic inelastic collision the kinetic energy of the system decreases but the momentum is conserved
This means that the (vector) sum of the final velocities must be equal to the total initial velocity (i.e. it is equal to the initial velocity of the incoming particle).This means that the vector diagram is a right angled triangle, where the truck moving east and north can be shown as base and perpendicular respectively And the hypotenuse is the final velocity of system after collision.
Velocity of truck moving in North (h) = 16m/s
Velocity of the truck moving in East (b) = 21m/s
By Applying the Pythagoras theorem,
the final velocity of the system after collision (h) = √[b^2+h^2]
= √[21^2 + 16^2]
= √[441+256]
= √697
= 26.4m/s
if glider 1 is moving at 6.0 m/s and glider two is stationary (not moving), what will happen when they collide?
After the two gliders collide with each other, both the two gliders start to move as a single body and it moves with a speed of 3m/s.
The glider 1 is moving with velocity,v₁= 6m/s. The glider 2 is stationary so, v₂=0. After the collision, both the two gliders stick to each other and start moving as a single body. If the mass of both the glider is the same and is equal to m. According to the conservation of momentum, the initial momentum will be equal to the final momentum. The initial momentum is, pi= m×6+ m×0=m×6. The final momentum after the collision is, pf=(m+m)×v=2m×v. Now, pi=pf, 6m=2m×v, v= 3m/s.
So after the collision both the gliders move together at a speed of 3m/s.
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a space vehicle is traveling at 4,000 km/h with respect to the earth when the exhausted rocket motor is disengaged and send backward with a speed of 80 km/h with respect to the command module. the mass of the motor is four times the mass of the module. calculate the speed of the command module after the separation.
The speed of the command module after the separation can be calculated using the conservation of momentum which is 3920km/h.
Since the motor is four times the mass of the command module, the total momentum of the system before the separation is
4×4000 km/h. After the separation, the motor has a momentum of 80 km/h and the command module has a momentum equal to the total initial momentum minus the momentum of the motor. Therefore, the speed of the command module is
4×4000 km/h - 80 km/h = 3,920 km/h.
Thus, the speed of the command module after the separation is 3,920 km/h.
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The water level on a beach wall is given by d(t)=6+4 cos (π/6.t - π/3)where t is the number of hours after midnight and d is the depth of the water in metres. a Sketch the graph of d(t) for 0≤t≤24. b What is the earliest time of day at which the water is at its highest? c Find the average rate of change of the depth of the water with respect to time between 3 a.m. and 9 a.m. d Find the rate of change of the depth of the water at time t hours after midnight. e Find the times at which the magnitude of this rate of change reaches its maximum value, and state the maximum value.
a. The water level on a beach wall can be modeled by the equation d(t)=6+4cos(π/6.t - π/3). The graph of this equation represents the water level variation over time, with t being the number of hours after midnight.
b. The graph is a sinusoidal wave with a maximum height of 10 meters and minimum height of 2 meters.
c. The earliest time at which the water is at its highest is 12:00 p.m. at which point d(t) = 10. The average rate of change of the depth of the water with respect to time between 3 a.m. and 9 a.m. is zero, as the water level is at its minimum during this time period. d. The rate of change of the water level with respect to time at any point t is given by the derivative of the function d(t), which is -4π/6 sin(π/6.t - π/3).
e. The magnitude of this rate of change reaches its maximum value of 4π/6 = 2.094 m/hr at times t = (3nπ + π/3)/(π/6), where n is an integer. The equation maximum value of the magnitude of the rate of change is 2.094 m/hr, and the water level is changing fastest at these times.
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what are recording meters used to detect?
Recording metres are used to detect voltage or current or both for a single phase. A kilowatt-kiloVARs recording meter will record true power (kilowatts) or reactive power (kiloVARs) on a time share basis.
A device that is typically powered by clockwork and has a chart on which fluctuations (such as current or pressure) are recorded.
The term recording instrument refers to a device that continuously records the magnitude variation of an electrical quantity over a specified time. It is utilised in settings where it is necessary to continuously monitor the state of the circuit. The record is utilised for computational or future reference purposes.
The graphed readings of the physical values are taken by the recording devices. Additionally, it keeps track of how the amounts change over time. Examples of recording instruments include the galvanometer recorder, thermoscope, ECG machine, and voltmeter.
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A non-uniform rod XY of ma 40 kg and 5. 0 m lie on the horizontal ground. It centre of gravity i 2. 0 m from the end x. Calculate the vertical force P, that will jut be ufficient to meet the end why from the ground. Why would the force P, if applied at the end X not be ufficient to lift the end X from the ground ?(g =10. 0 m/²)
The force required to just lift the Y end from the ground is 160 N, this force would not be sufficient to lift the X, as it is less than the reaction force at X.
Mass of the XY road, m = 40 kg
Weight of the road, W = 40×10 = 400 N
length of the rod, l = 5.0 m
Center of gravity is 2.0 m from the X end.
Let the vertical force required is P. Then taking the moment about x-axis.
P × 5 = 400 × 2
P = 160 N
Now, the downward force on X axis, = (400 × 3)/5 = 240 N
As downward force 240 N is more than the vertical force 160 N. So, it will not be sufficient to lift the X-end from the ground.
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Directions: Select one of the players you identified with most. Imagine you are them. Now, write a letter (1 paragraph) as if you were them to their parents telling them. of their experiences of training for the Olympics.
The ancient Greek sporting festival known as the Olympic Games was recreated in the late 19th century.
What is Olympics?Prior to the 1970s, the Games were only officially open to athletes with amateur status; however, in the 1980s, many events were made available to athletes with professional status.
The Games are currently accessible to everyone, including the best professional basketball players and football players (soccer). Several of the sports that are now a part of the Summer Games schedule, which at times has featured competitions in as many as 32 sports, were part of the ancient Olympic Games.
The Winter Games were approved for winter sports in 1924. The Olympic Games are now regarded as the top sporting event in the globe.
Therefore, The ancient Greek sporting festival known as the Olympic Games was recreated in the late 19th century.
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the ∆hfus for solvent a is 10.0 kj/mol and the ∆hsub is 40.5 kj/mol. what is ∆hvap for solvent a? report your answer in kj/mol and round to the first
The ∆H fus for solvent a is 10.0 kj/mol and the ∆H sub is 40.5 kj/mol, then the enthalpy change of vaporization or ∆H vap for solvent A is 50.5 kJ/mol.
The enthalpy change of vaporization (∆H vap) of a solvent can be calculated using the following equation:
=> ∆H Vaporization = ∆H Fusion + ∆H sublimation
here ∆H fus is enthalpy change of fusion (melting)
and ∆H sub is enthalpy change of sublimation (direct transition from solid to gas).
Given that:-
∆H fus for solvent A is 10.0 kJ/mol,
∆H sub is 40.5 kJ/mol,
Now, ∆H vap for solvent A can be calculated as follows:
=> ∆H vap
= ∆H fus + ∆H sub
= 10.0 kJ/mol + 40.5 kJ/mol
= 50.5 kJ/mol
So, the enthalpy change of vaporization for solvent A is 50.5 kJ/mol. This means that it takes 50.5 kJ of energy to convert 1 mole of solvent A from a liquid to a gas at its boiling point.
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when stopping for a train, stop at least ______ feet away from the tracks. drivers ed
"When stopping for a train, stop at least 15 feet away from the tracks."
When there is a stop sign at a railway crossing, the driver must stop completely between five and fifteen metres (50 and 50 feet) away from the nearest rail. Until you are certain that no trains are coming, do not move forward.
At many rail crossings, red light signals are combined with railroad signs. When the bells start to ring and the lights start to flash, stop because a train is coming. The driver of the car closest to the crossing must come to a complete stop at least five metres away from the nearest rail. Continue only until the train has past or has completely stopped, the lights, bells, and the train itself have all ceased. Make sure all the tracks are clear before crossing if there are multiple tracks.
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the wavelength of a certain laser is 0.66 microns, where 1 micron = 1 x 10-6 m. what is this wavelength in nanometers? (1 nm = 10^-9m) ?
The wavelength in nanometers is 660 nm, if the wavelength in micron is 0.66 micron.
Micron is the unit of length measurement of the atomic level. It is equal to 10⁻⁶ m. It is denoted by μ. Whereas nanometer is also a unit of length measurement but shorter than the micron. it is denoted by "nm". It is 1000 time shorter than the micron. 1 nanometer is equal to 10⁻³ micron or 10⁻⁹ meter. Both these units are used in measuring the radius of atoms, orbital radius of electrons, wavelength of light waves, sound waves etc.
If the wavelength in micron = 0.66 micron = 0.66 × 10⁻⁶ m
Then wavelength in nanometer, = (0.66 × 10⁻⁶)/(10⁻⁹) = 660 nm
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A freight train traveling with a speed of 10.0m/s begins braking as it approaches the train yard. The train’s acceleration while braking is -0.1m/s2. What is the train’s speed after 30s?
The final speed of the train after 30 seconds with an acceleration of -0.1m/s² is 7 meter per second.
What is Negative acceleration?Acceleration is the rate of change of velocity of a moving body with respect to time, and when the change in the velocity of an object is decreasing, it is called as negative acceleration. Negative acceleration is also called as the de-acceleration or deceleration of the object.
Acceleration = Rate of change in velocity
a = (v-u)/t
a = -0.1m/s²
u = 10m/s
t = 30 seconds
v = ?
a = (v-u)/t
at = v-u
v = u + at
v = 10 + (-0.1) × 30
v = 10 + (-3)
v = 10-3
v = 7 m/s
Therefore, the final speed of the train after 30 seconds is 7 meter per second.
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Classify the statements as correct or incorrect.
A. A thermometer measures the average kinetic energy of a substance.
B. Convection occurs only in liquids and gases.
C. Heat is a form of energy.
D. All substances radiate heat.
E. Heat flows from a colder substance to a hotter substance.
F. Our body temperature is always equal to the temperature around us.
Correct or incorrect
Answer:
A. True
B. ?
C. True
D. False
E. False It is complete opposite
F. ?
digital circuits fail because the ? is lost somewhere between the circuit input and output stages.
Digital circuits fail because the signal is lost somewhere between the circuit input and output stages.
A subfield of electronics called digital electronics is focused with the study of digital signals and the creation of digital signal-using or -generating systems. Boolean logic and discrete signal electronics are terms used to describe electronics, gadgets, and equipment.
Any circuit with a signal that must fit into one of two distinct levels is said to be digital. Each level is represented by one of two states (for instance, on/off, 0/1, true/false). Digital circuits create logic gates using transistors to perform Boolean logic.
In digital electronics, there are primarily two types of digital logic circuits. Sequential logic circuits and combinational logic circuits are what they are.
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Describe how you could show that the strength of an electromagnet depends on the current in the coil.
Answer:
The strength of the current passing through the coil, the greater the current, the greater the strength. This because the current increases there is more flow of electrons which in turn increases the magnetic field around it. The number of turns in the coils, the greater the number of coils, the greater the strength.
Explanation:
sorry if im wrong
correct answer isss??
Answer:
A) 5.2 A
Explanation:
formula = watts ÷ volts
1200 ÷ 230 = 5.217
if you punch the table top, your hands hurts because the table pushed back against your hand. you know this because your hand did not go through the table. with what type of force did the table push?
The type of force that the table push is the same force but in the opposite direction of your punch.
If you punch a stationary object, such as a table or a wall, your hands will feel hurt because the object exerts the same amount of force, but in the opposite direction of your punch. The physics law that applies to this phenomenon is Newton's third law of motion. The law sounds as follows:
If two bodies exert forces on each other, these forces have equal magnitude but in opposite directions.
In the example above, the action is your punch to the object and the reaction is the force that the object exerts caused by your punch. If you punch a wall with a force of 200 N, the wall imparts a force back to your hands of 200 N, which is why it feels hurt.
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how much energy must be used to produce 4.75 mol of gaseous water?: h20 (l) 44.0 kj -→ h2o (g)
The amount of energy required to produce 4.75 moles of gaseous water is 198.5 kJ.
The energy required to produce gaseous water from liquid water is given as 44.0 kJ/mol. This means that for every mole of liquid water that is converted to gaseous water, 44.0 kJ of energy must be added to the system.
To find the total energy required to produce 4.75 moles of gaseous water, we simply multiply the energy per mole by the number of moles:
Energy = 44.0 kJ/mol * 4.75 moles = 208.5 kJ
So, 208.5 kJ of energy must be added to the system to produce 4.75 moles of gaseous water from liquid water.
This energy is used to break the hydrogen bonds between the water molecules in the liquid and to increase the kinetic energy of the water molecules so that they have enough energy to escape from the liquid into the gas phase.
The energy required to produce gaseous water from liquid water is an example of an endothermic process, which means that energy must be added to the system for the process to occur.
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what is acceleration
A particle is constrained to travel along the path. If x = (4t4) m, where t is in seconds, determine the magnitude of the particle's velocity and acceleration when t = 0.5 s.
The required magnitude of velocity and acceleration are calculated to be 2 m/s and 12 m/s² respectively.
The position of the particle is given as, x = 4t⁴
We know the velocity, V = dx/dt
dx/dt = d/dt (4t⁴) = 16 t³
The velocity at t = 0.5 s is given as,
V = 16 t³ = 16 × 0.5³ = 2 m/s
Acceleration function A = dV/dt
dV/dt = d/dt(16 t³) = 48 t²
A = 48 t² = 48(0.5)² = 12 m/s²
Thus, the magnitude of velocity and acceleration are calculated to be 2 m/s and 12 m/s² respectively.
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a 1050 kg car has a velocity of 2.65m.s^-1 north. the car hits the rear of a stationary truck,the bumpers lock together. the velocity of the car-truck system immediately after the collision is 0,78m.s^-1 north. calculate the mass of the truck?
The mass of the truck is 1020 kg.
Calculate the mass of the truck?The steps for this process are as follows:
Step 1: Let m1 and m2 be the masses of the car and truck respectively.
Step 2: According to the law of conservation of momentum,
m1v1 + m2v2 = (m1 + m2)vf,
where v1 and v2 are the initial velocities of the car and truck respectively, and vf is the final velocity of the car-truck system.
Step 3: Substitute the given values in the equation to get m2 = 1020 kg.
Step 4: Hence, the mass of the truck is 1020 kg.
The law of conservation of momentum is used in this question. According to the law of conservation of momentum, the total momentum of a system remains constant, regardless of external forces. In this question, the law of conservation of momentum is used to calculate the mass of the truck by equating the total momentum of the system before and after the collision.
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The height of a satellite at perigee is 300 km above the earth's surface and it is 3000 km at apogee. Find the orbit's eccentricity. If we take the orbit to define the xy plane and the major axis in the x direction with the earth at the origin, what is the satellite's height when it crosses the y axis? The earth's radius is Re = 6.4 Times 10^6 m. You will also need to know GM_e, but you can find this if you remember that GM_e / R_e^2 = g.]
Satellite moves in an elliptic orbit with Earth being in one focus.
The orbit's eccentricity is 0.1677
we know that
|CF|=|FB|=R=6400|PC||AB||FC|=300=3000=|FB|=R=6400
unit of km has been omitted, we will restore it in the end. let a and b be semi-major and semi- minor axes of the ellipse. Let c be the distance from the focus, we have
2a = |AB|+2R+|PC| = 2R+3300
a =8050 = C+R+ |PC|
=c+6700
c = 1350
Since eccentricity is defined as e = c/a combining (4) and (5) we find
13508050 = 0.1677 e =ac=80501350= 0.1677
We can find b from the known relation 2b = c2-a2.
since we have a and b, we can set up the ellipse equation as
a2(x-c)2 + b2y2 = 1
we can set x = 0 and solve for y in equation(7)
y = a (1-a2c2) = a(1-e2)
= 7800
satellite's height is h, then h = y-R
h = y- R = 1400 km
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a 28 kg child on a swing is traveling at 4.2 m/s. what is his gravitational potential energy if he has 315 j of mechanical energy? (answer: 68j)
The child on the swing has 68 J of gravitational potential energy.
The total mechanical energy, E, of a system can be expressed as the sum of its kinetic energy, KE, and its gravitational potential energy, PE:
E = KE + PE
Given that the child on the swing has 315 J of mechanical energy and is traveling at a velocity of 4.2 m/s, we can calculate his kinetic energy as follows:
KE = 0.5 * m * v^2 = 0.5 * 28 kg * (4.2 m/s)^2 = 89.64 J
Next, we can use the total mechanical energy equation to solve for the gravitational potential energy:
E = KE + PE
315 J = 89.64 J + PE
PE = 315 J - 89.64 J = 225.36 J
In the case of the child on the swing, the height of the swing is not specified, so we cannot calculate the gravitational potential energy based on height. However, we can still find the gravitational potential energy by using the total mechanical energy, which is the sum of the kinetic energy and the gravitational potential energy.
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