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.

Options

A. The direction of motion of the ball changes every 10.
B. Speed of ball changes every 10
C. Average speed of ball over any 20 interval is fixed.
D. The acceleration of ball is the same as from the train

Answer

B, C

Explanation

In this problem, it is important to understand the frame of the observer. Here we are considering the motion from the ground. The velocity of trains (10 m/s) is greater than the speed of ball (1 m/s). Relative speed of the ball before collision with side of train is 10 + 1 = 11 m/s.
(Opposite direction) Relative speed after collision with side of train = 10- 1 = 9 m/s. (Same direction) As speed is changing after travelling 10 m and speed is 1 m/s hence, time duration of the changing speed is 10.
Since, the collision of the ball is perfectly elastic there is no dissipation of energy hence, total momentum and kinetic energy are conserved. Since, the train is moving with constant velocity hence, it will act as inertial frame of reference as that of Earth and acceleration will be same in both frames.
We should not confuse with non-inertial and inertial frame of reference. A frame of reference that is not accelerating will be inertial.