Consider the falling object of mass 10 kg in Example 2 but assume now that the drag force is proportional to the square of the velocity. a. If the limiting velocity is 49 m/s (the same as in Example 2), show that the equation of motion can be written as dv dt 245 (492 – 12) Also see Problem 21 of Section 1.1. b. If y(0) = 0, find an expression for ( 1 ) at any time. c. Plot your solution from part b and the solution (26) from Example 2 on the same axes. d. Based on your plots in part e, compare the effect of a quadratic drag force with that of a linear drag force. c. Find the distance x(t) that the object falls in time t. f. Find the time T' it takes the object to fall 300 m.

Finding the slope of both the velocity-time graph is necessary in graphs in order to compute an object's displacement.

When there is displacement, an object's position as relation to a stationary reference alters. For instance, when a player strikes a pool ball, it goes from one place to another. It is said to be misplaced. There is a magnitude and a direction to the vector quantity displacement.

A defense tactic called displacement involves someone shifting their unpleasant emotions of one thing or person to another. A person who is angry about their job, for instance, might rage at a family person in order the "take it out" on them.

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[tex]E = \frac{K Q q }{ \sqrt[\frac{3}{2} ]{ R^{2} + x^{2} } }[/tex]The magnitude of electic field at a distance 'a'  from the center of the ring is

[tex]E = \frac{K Q q }{ 2\sqrt{2} a^{2} }[/tex]  where  K =  [tex]\frac{1 }{4 \pi }[/tex]∈

a = radius of ring  

Q = uniform charge distribution over ring

q =  another point charge located at a distance a from centre of ring

We know that the electric field at distance x from the center of ring of radius R is given by

[tex]E = \frac{K Q q }{ \sqrt[\frac{3}{2} ]{ R^{2} + x^{2} } }[/tex]

according tho the question the radius of ring is equal to distance of q from centre of the ring

substituting  R= a , x = a

we get

[tex]E = \frac{K Q q }{ \sqrt[\frac{3}{2} ]{ a^{2} + a^{2} } }[/tex]

[tex]E = \frac{K Q q }{ \sqrt[\frac{3}{2} ]{ 2 a^{2} } } }[/tex]

[tex]E = \frac{K Q q }{ 2\sqrt{2} a^{2} }[/tex]

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Answer:

Below

Explanation:

From the top graph her acceleration is -3 m/s^2 at the point in question

From the lower graph at time t = 3 s  her velocity = 5 m/s

vf = vo + at

   =  5 m/s  + (-3)(.73)          <====3.73 s is .73 s past the 3 s mark

   =  2.81 m/s

The option that best describes why you can analyze this event using conservation of momentum, is The throwing action is quick enough that external forces may be ignored. The best answer is A.

This is because the conservation of momentum is only applicable when the external forces acting on a system are negligible. In this case, the external forces can be ignored, so the conservation of momentum can be used to analyze the motion.

The conservation of momentum is a fundamental law of physics that states that the total momentum of a system is conserved, which means that the total momentum of a system remains constant. This means that if there are no external forces acting on the system, the momentum of the system will not change. This law is particularly useful for analyzing the motion of objects, and can be used to calculate the velocity, acceleration, and other parameters of an object's motion.

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The moment of inertia is represented by the following equations if we consider the earth to be a solid sphere spinning about its center:  I ≈ 9.736 ×  (10)37 kgm2.

Taking into account that the earth's radius is 6.38  *1 0 6 m and its mass is 5.98 * 10 24 kg

The moment of inertia is represented by the following equations if we consider the earth to be a solid sphere spinning about its center:

I = 2 / 5  M R²

When the earth's radius is R and its mass, M,

This information is provided to us:

↦ M = 5.98 × (10 )24 kg

↦  R = 6.38 × (10) 6 m

With the aforementioned equation updated to include these values:

I = 2 / 5 ( 5.98 × (10 )24 kg ) ( 6.38 × (10)6 m )²

⇒  = 2 / 5 ( 5.98 ×  (10)24 kg ) ( 4.07044 × (10) 13 m ²)

⇒ 2 / 5 ( 2.4341 ×  (10 )38  kg m 2 )

⇒  = 9.736 ×  (10 )37 kg m 2.

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According to the question, the answer of distance will be:

a. Your displacement is 0 m.

b. The total distance traveled is 3408 m.

c. Your displacement is 0 m.

d. The total distance you have traveled since first leaving your house is 3408 m.

What is distance?

Distance is the amount of space between two objects or points. It is usually measured in units of length such as kilometers, miles, meters, or feet.

a)Displacement is defined as the total distance in a specific direction, and since you did not move in any direction, your displacement is 0 m.

b) You traveled 1704 m to the store and 1704 m back to your friend's house, so the total distance traveled is 3408 m.

c) Displacement is defined as the total distance in a specific direction, and since you did not move in any direction, your displacement is 0 m.

d)  You traveled 1704 m to the store and 1704 m back to your house, so the total distance you have traveled since first leaving your house is 3408 m.

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According to the utilitarian ethical theory, morality is decided by emphasising results.

This kind of consequentialism exists here. According to utilitarianism, a decision should be made if it would result in the greatest amount of benefit for the largest number of people. The utilitarian perspective holds that you should select the ice cream flavour that would make you feel the happiest if you are making a decision for yourself.

A variation of consequentialism known as utilitarianism holds that actions' results are the only criteria for what is right and bad. Utilitarianism takes into account the interests of every sentient being equally, unlike other consequentialist ideologies like egoism and altruism.

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Answer:

Below

Explanation:

The heat the water gains is the heat lost by the metal ...

  Hw = .25 kg * (28- 20 C) * 4180 J/(kg K) = 8360 J

So the metal gains 8360 J and cools by 25 °C

500g = .5 kg

                        8360 /(.5kg* 25 C) = 668.8 J /(kg K)

Note: Remember that a degree C = one K)  

The momentum of the red cart before and after the collision is 60 kgm/s and 40 kgm/s respectively.

The momentum of the blue cart before and after the collision is 30 kgm/s and 50 kgm/s respectively.

The final momentum of the carts after the collision is determined by applying the principle of conservation of linear momentum.

Sum of initial momentum = sum of final momentum

60 kgm/s  +  30 kg m/s  = 50 kgm/s  + Pr

where;

90 kgm/s - 50 kgm/s = Pr

40 kgm/s = Pr

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PART A:

-9.8 m/s^2 (S)

PART B:

0 meters (N)

PART C:

≈ 7.7 (ROUNDED)
Accurate: 7.69300

PART D:

4.9 m (Δy)

Transcribed Text:
A tennis player tosses a tennis ball straight up and then catches it after 1.57 seconds at the same height as the point of release.

Required:

Use the following kinematic equations:

[tex]v=v_o+at[/tex]

Final velocity = Initial Velocity + Acceleration × Time

Δ[tex]x=v_ot+\frac{1}{2}at^2[/tex]

Change in position (displacement) = Initial velocity × time + (0.5) (acceleration × final time)²

[tex]v^2=v_o2+2a[/tex]Δ[tex]x[/tex]

Final velocity (squared) = Initial velocity (two times) + (two times) acceleration * change in position

*A illustration shall be provided for better understanding*

Part A:

Once the tennis player releases the ball, the only force acting on that ball is the gravitational force which exerts an acceleration of -9.8 m/s^2.

Part B:

At that maximum height (as seen in the attached picture) would have a velocity of 0 for just a split moment making this the answer.

PART C: *Be aware that the PART A and B are just conceptual type questions and now we have actual calculations to figure out*.

Reviewing what we know,

Acceleration = -9.8 m/s^2

Time = 2.00 seconds

Now we have to find the initial velocity.

Reviewing the picture and the final velocity, it should turn out this way:

Looking at the kinematic equations we would use:
[tex]V_f=V_i+at[/tex]

Current equation:

[tex]-V_o=V_o+(-9.8)(1.57)[/tex]

* MULTIPLY -9.8 and 1.57!!!

Now we must subtract the V(naught) from both sides.

The left and right side would become:

[tex]-2v_o=-15.38600[/tex]

Divide -2 from both sides.

Initial velocity = 7.69300

Rounded

≈ 7.7 m/s

This would make the initial velocity equal to 7.7 m/s

PART D:
In order to solve for maximum height, we must use some values we would need to find this answer.

Initial velocity = 7.69300 m/s

Acceleration = -9.8m/s^2

Final velocity (or velocity at max height) = 0 m/s

Δy = ...

The kinematic equation we would be using is:

[tex]v^2=v_o2+2a[/tex]Δ[tex]x[/tex]

Because the situation is in the vertical dimension, the 'delta x' will be changed to:

[tex]v^2=v_o2+2a[/tex]Δ[tex]y[/tex]

Subtract the initial velocity squared from both sides of the equation.

This would give us:
[tex]v^2-v_0^2=2a[/tex]Δ[tex]y[/tex]

Divide both sides by 2a.

By finding this we can find the vertical displacement.

[tex]\frac{v^2-u^2}{2a}[/tex]=Δ[tex]y[/tex]

Let plug in the known values

[tex]\frac{(0)^2-(9.8)^2}{2(-9.8^2)} = 4.9m[/tex]

Done

A ball is thrown upwards and returns to the same position. Compared with its original speed after relase, its speed when it returns is about the same.

To solve this case, we will use energy conservation and free fall concepts.

Energy conservation defines that the energy in a system will remains the same as long as no other external force working in the system. Energy in a system will not be created or destroyed, but only change its form from one to another.

We will use the energy conservation concepts in this case under the kinetic and potential energies approach.

When the ball is thrown upwards, the ball has its kinetic energy and zero potential energy. As the ball goes higher, it will reach its highest peak once all of its kinetic energy has change into potential energy. The potential energy then will change into kinetic energy directly as the ball falls into its initial position. We can formulazid these moments as:

E1 = E2 = E3

where:

E1 = total energy when the ball is thrown upwards

E2 = total energy when the ball just stop at its highest peak

E3 = total energy when the ball starts to drop into its initial position

E1 = E2 = E3

Ek1 + Ep1 = Ek2 + Ep2 = Ek3 + Ep3

1/2 mv1² + mgh1 = 1/2mv2² + mgh2 = 1/2mv3² + mgh3

1/2mv1² + mg(0) = 1/2m(0)² +mgh = 1/2mv3² + mg(0)

1/2v1² = gh = 1/2v3²

v1² = v3² =2gh

v1 = v3 = √2gh

The ball will falls with the same speed as the speed when it was thrown upwards.

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Distance between two lines of grating is 4.85*10^-4 cm.

The act of bending light around corners where it spreads out and illuminates regions is known as the diffraction of light.

A optical element known as a diffraction grating splits light into numerous beams that move in various directions. The directions, as well as diffraction angles of these beams, depending on the wavelength of the incident light, the angle at which the wave strikes, and the distance or spacing between consecutive diffracting elements.

The distance between the two grating lines is calculated by taking the reciprocal of the grating value which is provided.

Distance between two lines of grating is, 1/2060 = 4.85*10^-4 cm.

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Answer:

a) To find the depth of the lake, we can use the following equation:

distance = initial velocity x time + (1/2) x acceleration x time^2

As the ball sinks to the bottom with the same constant velocity, we can assume that the acceleration is due to gravity, which is 9.8 m/s^2 (going downward)

We know that the time it takes for the ball to hit the bottom is 5.05 seconds, so we can substitute these values into the equation:

distance = 0 x 5.05 s + (1/2) x 9.8 m/s^2 x (5.05 s)^2

distance = 12.6125 m

So the lake is 12.6125 m deep

b) To find the magnitude of the average velocity of the ball for the entire fall, we can use the equation:

average velocity = distance / time

We know that the distance is the depth of the lake, which is 12.6125 m, and the time is 5.05 s, so we can substitute these values into the equation:

average velocity = 12.6125 m / 5.05 s

average velocity = 2.49 m/s

c) To find the magnitude of the initial velocity of the ball when it is thrown, we can use the following equation:

initial velocity = final velocity^2 + 2 x acceleration x distance

As the ball reaches the bottom in the same time as when it was dropped, 5.05 s, we can assume that the final velocity is 0 m/s. We know that the acceleration is 9.8 m/s^2 (going downward), and the distance is the depth of the lake, which is 12.6125 m. So we can substitute these values into the equation:

initial velocity = 0^2 + 2 x 9.8 m/s^2 x 12.6125 m

initial velocity = 24.6 m/s

Note that the magnitude of initial velocity is 24.6 m/s, which is a scalar value, it doesn't have any direction.

The equation you provided describes the relationship between the angle θ and the various physical parameters of the system.

The equation expresses the fact that the force of tension in the threads must balance the electrostatic force between the two charged balls.

On the left side of the equation, sin(θ) represents the component of the force of tension perpendicular to the thread, while tan(θ) represents the ratio of this component to the component of the force of tension along the thread.

On the right side of the equation, q represents the charge on each ball, while 16πε0 is the electric constant and g is the acceleration due to gravity. The product of these constants and the length of the threads squared, l^2, represents the electrostatic force between the balls. Finally, m represents the mass of each ball.

By equating these two sides, we see that the angle θ satisfies the relationship between the physical parameters described by the equation. As the charge q, length of the threads l, or mass m of the balls changes, the angle θ will vary accordingly in order to maintain balance between the tension and electrostatic forces

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Usability of the New E-mail System 1. Substitute a more descriptive scale, such as "Strongly Agree," "Agree," "Somewhat Agree," "Somewhat Disagree," "Disagree," and "Strongly Disagree" for the numerical scale.

Simply remove the numerical scale and insert the more descriptive scale in its place to do this. The first sentence, for instance, may be altered to read "I can work more quickly and efficiently in my work group since we use the new e-mail system. Use the following scale to indicate your level of agreement with this statement: Strongly Agree, Agree, Somewhat Agree, Somewhat Disagree, Disagree, Strongly Disagree."

2. Ensure that the questions are precise and short.

You must make sure the questions are simple to grasp, not too long or difficult to answer, and plain and succinct. For instance, you could reword the survey's second statement to read, "Does using the new e-mail system boost my work performance?"

3. Check if the survey's questions are pertinent to the subject at hand.

The survey topic should be addressed by the questions. The survey in this instance concerns how usable people believe the new email system to be. Therefore, this subject should be the subject of all queries. The third statement in the survey has to be changed or removed because it has nothing to do with the subject matter.

4. Only posit inquiries that can be fully answered.

The questions ought to be created in a way that allows for truthful responses. The inquiries must to be clear and devoid of any possibility for interpretation. The fourth line, for instance, may be changed to read, "Using the new e-mail system makes it easier for me to prepare for meetings and finish my work on time?"

5. If necessary, give the questions context.

It could occasionally be required to provide the questions background. How simple is it for you to use the new e-mail system to get ready for meetings and finish your work on time, for instance, is how the fifth sentence may be phrased.

6. Lower the overall number of inquiries.

It's crucial to limit the overall number of inquiries to minimum.

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No The distance travelled by the body can never be greater than the magnitude of the displacement.

The displacement cannot be more than the distance because the distance is defined as the total amount of path covered by a moving body in a given time period, whereas the displacement is defined as the linear amount of path covered by a moving body in a given time period.

The shortest path and the entire path traversed on a straight road without turning are the same. As a result, if the automobile is traveling in a straight line without changing direction, the distance traveled and amount of displacement are equal. The resulting shaking has a wide range of values that vary depending on distance, surface material, and other factors.

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Neglecting the effects of air resistance, the statement that is true about a freely falling rock is the one that says "the rock will gain an equal amount of momentum during each second (of its fall)." Therefore, the correct answer is option A.

According to the question, a rock is dropped from a tower. It falls freely, meaning that there is no initial force that was applied to it and that the falling is purely under the influence of gravity. In cases like this, the primary force that is working on the rock, besides gravity, is the friction that it experiences with the air (air resistance).

Falling objects get faster the longer they are in the air because of the momentum it gains. Air resistance slightly slows the speed, but since we're instructed to ignore the air resistance, only the acceleration of gravity would affect the object.

The formula you can use to calculate a falling object is:

  v = g * t

  v = 2 * g * h

  h = 0.5 * g * t²

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The rate of change in velocity is known as acceleration.She thereby accelerated 0.027 m/s2 throughout her strong effort.

The rate of change in velocity is known as acceleration.Acceleration typically signals a change in speed, though this is not always the case.

Because of the shifting direction of its velocity, an item moving on a circular path at a constant speed is still accelerating. The change in velocity divided by the time interval during which that change happened is the definition of acceleration (in its simplest form).

The formula is: a= v2 - v1 /t

Where:

Initial velocity is v1.

v2: final speed

t: the amount of time required for that acceleration

introducing the specified values into the equation

a=0.027 m/s2

where

a = 3.5 m/s - 31 m/s /15 m/s

She thereby accelerated 0.027 m/s2 throughout her strong effort.

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The correct sequence is 5, 1, 3, 8, 4, 6, 7, 2. The statement that is being discussed is:

"For all > 0 there exists a > 0 such that for all satisfying we have that ."

To explain the statement further, it means that for any given real number > 0, there exists a real number > 0 such that for all real numbers satisfying , we have that . In other words, if is sufficiently close to (i.e. if is less than ), then must also be close to (i.e. must be less than ).

This idea is essential to understanding limits. The statement can be written more formally as:

[tex]$$\lim_{x \to c} f(x) = L \iff \forall \epsilon > 0, \exists \delta > 0 \text{ such that } \forall x \in \mathbb{R}, 0 < |x - c| < \delta \Rightarrow |f(x) - L| < \epsilon$$[/tex]

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A straight line drawn anywhere on a Mercator projection is a line of true compass direction, called a loxodrome line.

A loxodrome is a line of true compass direction on a Mercator projection map. Here are some key points to keep in mind:

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a.  The acceleration of the 4.00 kg crate is 3.75 m/s^2.

b.  A free-body diagram for the 4.00 kg crate is shown below:

4.00 kg

T

c. The direction of the force is to the right, since the crate is moving to the right. The magnitude of the force is 15 N.

Acceleration can be described as  the rate of change of the velocity of an object with respect to time.

We use  Newton's second law of motion, which states that the net force on an object is equal to its mass times its acceleration

(F_ = m * a).

The total force on each crate is equal to the force applied on it. If the force applied on the 6.00 kg crate produces an acceleration of 2.5 m/s^2, the  total force on the 6.00 kg crate is 6.00 kg * 2.5 m/s^2 = 15 N.

Therefore, the total  force on the 4.00 kg crate is 4.00 kg * a = 15 N,

a = 15 N / 4.00 kg

a = 3.75 m/s^2.

The tension T in the rope that connects the two crates can be found using Newton's second law of motion.

b.  (F = m * a), so we can put out the  the equation as :

T - 4.00 kg * 3.75 m/s^2 = 0

T = 4.00 kg * 3.75 m/s^2 = 15 N

c.

F - 6.00 kg * 2.5 m/s^2 = 0

F = 6.00 kg * 2.5 m/s^2 = 15 N

The direction of the force is to the right, since the crate is moving to the right. The magnitude of the force is 15 N.

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To calculate the force on the point mass m placed at the center of the semicircle, we need to consider the gravitational force acting on the mass m due to the uniform rod.

The gravitational force acting on the point mass m can be calculated using the equation:

F = G * (m * M) / R^2

where G is the gravitational constant, m is the mass of the point mass, M is the mass of the uniform rod, and R is the radius of the semicircle.

The uniform rod can be considered as a point mass located at the center of the semicircle, so the force on the point mass m can be simplified as:

F = G * (m * M) / R^2 = G * m * M / R^2

In conclusion, the force on the point mass m placed at the center of the semicircle is equal to the gravitational force between the point mass and the uniform rod, which is given by the equation F = G * m * M / R^2.

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The formula y = - 1 2 g t 2 y = - frac 1 2 g t 2 y=-21gt2 describes the vertical distance from the ground, where g is the acceleration of gravity and h is a height.

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Your heart stops beating, your breathing stops, and your brain stops working. According to research, brain activity may continue for several minutes after a person is declared dead.

Visual or auditory hallucinations are common during the dying process. The reappearance of deceased family members or loved ones is common. These visions are thought to be normal.

The dying may shift their focus to "another world," where they may converse with people or see things that others do not.

Thus, brain activity is not synonymous with consciousness or awareness. It does not imply that the individual is aware that they have died.

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The current sensitivity of a moving coil galvanometer increases with a decrease in its resistance.

What is Current Sensitivity?

Current sensitivity is a measure of the responsiveness of an instrument to the current flowing through it. In particular, it is the deflection produced by a given amount of current passing through a device. The higher the current sensitivity, the smaller the amount of current required to produce a given deflection, and thus the more sensitive the instrument is to changes in current.

This is because the current sensitivity of a galvanometer is defined as the deflection produced per unit of current passed through it. Therefore, a higher current sensitivity means that a smaller current can produce a larger deflection, which can be achieved by decreasing the resistance of the galvanometer. This is because a lower resistance will allow a larger current to flow through the coil, which will result in a larger deflection of the coil.

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Answer:

Resistance

Explanation:

Sensitivity of a moving coil galvanometer can be increased by increasing the number of turns in the coil, the area of coil and magnetic field whereas by decreasing the couple per unit twist of the suspension.

Students monitor the progress of a marble by measuring its speed and distance travelled. They calculate the speed using the formula Speed = Distance / Time.

How do you find the velocity of a marble?

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By the use of law of reflection To get a complete view of the rear window of the car is enough for the rear-view mirror to have a height of 0.1137m or 11.37cm

According to the law of reflection, the angle of incidence and reflection is equal.

[tex]\theta_r=\theta_i[/tex]

Both the incident and reflected rays lay on the same plane.

Plane mirrors are reflective surfaces where each point of the mirror has the same normal direction to the surface. As a result, the size of the images produced by flat mirrors is equal to that of the object, and the image's distance is equal to that of the object.

Mathematically, the plane mirror equation yields,,

[tex]i=-o[/tex]

The virtual nature of the image is represented by the negative symbol. The plane mirror's lateral magnification is,

[tex]m=\frac{-i}{o}[/tex] = 1.

We are assuming that the top of the mirror, with unknown height

h, matches the driver's eyes. The height of the window is

H= 0.55m, while the distances from the mirror to the eyes and from the window to the mirror are d=0.60m and D=1.70m, respectively.

The following is how the reflection process works: An angle is created when a light beam from the window hits the mirror, reflected on the road, reaches the driver's sight. The worst case scenario occurs at the window's angle's lowest point. [tex]\theta_r[/tex],  . The mirror's height must be adjusted to guarantee that the reflected light hits the driver's eyes.

. Using the trigonometric relations,[tex]Tan \theta=\frac{H-h}{D+d}[/tex]

for the large lower triangle, and,

[tex]Tan \theta=\frac{h}{d}[/tex] for the small upper one.

Equating the tangents results in the equation,

 [tex]\frac{h}{d}=\frac{H-h}{D+d}[/tex]

solving for h

h=[tex]\frac{Hd}{D+2d}[/tex]

Substituting the numeric values,

[tex]h=\frac{0.55m\times0.60m}{1.70m +2\times0.60m}[/tex]

h=0.1137m

To get a complete view of the rear window of the car is enough for the rear-view mirror to have a height of 0.1137m or 11.37cm

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The total electric field at a point inside the shell is, [tex]E = \dfrac{kq}{r^{2}}[/tex].

Consider the point P placed inside the shell. As shown in the figure above, the Gaussian surface is said to have a radius r. The Gaussian surface contains no charge inside it.

Hence, q = 0

Therefore,

E = 0

It can be conclude that the field inside the spherical shell is always zero.

The electric field due to point charge q placed at the center at a point which is at a distance r from the center (inside the shell) is given by,

[tex]E = \dfrac{kq}{r^{2}}[/tex]

where, k is the permittivity of free space.

Hence, the total electric field at a point inside the shell is,

[tex]E = \dfrac{kq}{r^{2}}[/tex]

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