A ball is thrown upward in the air by a passenger on a train that is moving with constant velocity. (a) Describe the path of the ball as seen by the passenger. Describe the path as seen by a stationary observer outside the train. (b) How would these observations change if the train were accelerating along the track?

The equation for trajectory of projectile is given as,

$y=x\tan \theta -\frac{g{x}^2}{2u^2{\cos }^2\theta } .........................\left(1\right)$

Here,

x is horizontal position.

y is the vertical position,

u is the initial velocity of projectile.

g is gravitational acceleration.

$\mathit{\theta }$ is the angle of projection.

From equation 1, it is observed that trajectory of projectile (y) depends on the acceleration due to gravity, initial velocity and angle of projection.

a.

Hence it the ball is thrown upward in the air by a passenger on a train that is moving with constant velocity then the trajectory of the ball will be a straight line which goes straight up and come back down because both passenger and the ball moving with the same constant velocity.

But for the stationary observer outside the train, the ball is a projectile that follows a projectile motion because the ball has an initial velocity which is projected at some angle $\mathit{\theta }$. This happens only because there is no relative motion between both.