Question

A ball is bouncing elastically with a speed 1 𝑚/𝑠 between walls of a railway compartment of size 10 𝑚 in a direction perpendicular to walls. The train is moving at a constant velocity of 10 𝑚/𝑠 parallel to the direction of motion of the ball. As seen from the ground,

• A. the direction of motion of the ball changes every 10 seconds.
• B. average speed of ball over any 20 second interval is fixed.
• C. speed of ball changes every 10 seconds.
• D. the acceleration of ball is the same as from the train.

Answer 1

Answer: (B), (C), (D)

the acceleration of ball is the same as from the train.

As time is independent of reference frame so, Time of collision between two walls

$t=\frac{\Delta x}{v_{BT}}t=\frac{10m}{1m/s}=10s$

Speed of ball changes every 10 seconds after every collision.

After elastic collision with wall 𝐼

$v_{BT}=-1i$

$v_{BG}=-1i+10i=9i$

moving along positive direction


After elastic collision with wall 𝐼𝐼

$v_{BT}=1i$

$v_{BG}=1i+10i=11i$

moving along positive direction

Hence, speed of ball with respect to ground frame does change every 10 seconds but not the direction.

Average speed of ball

$v_{avg}=\frac{totaldistance}{Totaltime}$

$v_{avg}=\frac{9\left(10\right)+11\left(10\right)}{10+10}$

$=\frac{200m}{20s}$

= $10m/s$

It is constant in every 20 𝑠
Acceleration of the ball is zero as it is moving with constant velocity.

Final Answer: (𝒃), (𝒄), (𝒅)