Question

A ball is thrown from the rear end of the compartment of the train to the front which is moving at a constant horizontal velocity. An observer A sitting in the compartment and another observer B standing on the ground drew the trajectory. They will have

A. equal horizontal and equal vertical ranges.

B. equal vertical ranges but different horizontal ranges.

C. different vertical ranges but equal horizontal ranges.

D. different vertical ranges and different horizontal ranges.

Answer 1

Recall the kinematic equation for the range of the projectile and determine on which factor the range depends. The acceleration due to gravity does not affect the horizontal motion of the body.

Complete step by step answer:

According to the kinematic equation relating displacement, initial velocity, acceleration and elapsed time, we can express the vertical and horizontal ranges of the ball.

$S = ut + \dfrac{1}{2}a{t^2}$

Here, S is the displacement, u is the initial velocity, a is the acceleration of the ball and t is the time.

By taking the horizontal component of the initial velocity we can get the horizontal range and by taking the vertical component of the initial velocity of the ball, we can get the vertical range.

Therefore, the range depends on the initial velocity of the ball.

In the vertical direction, the acceleration of the ball is due to the acceleration due to gravity in the opposite direction.

$a = - g$

There is no component of acceleration due to gravity in the horizontal direction of the ball because acceleration due to gravity acts only in the vertical motion of the object.

For the vertical motion of the ball, the value of acceleration due to gravity is the same for both A and B. therefore, the vertical range will be the same for both observers.

In the horizontal direction, the initial velocity of the ball for an observer standing on the ground is the sum of velocity of the train and velocity at which the ball is thrown. The initial velocity for the observer sitting inside the compartment is only due to velocity at which the ball is thrown because he is also moving with the train.

Therefore, the horizontal range will be greater for observers standing on the ground.

So, the correct answer is “Option B”.

Note: The velocity of the ball thrown by the observer in the compartment is due to the combined effect of velocity of the train and the velocity at which the ball is thrown.