Question

A person sitting at the rear end of the compartment throws a ball towards the front end. The ball follows a parabolic path. The train is moving with uniform velocity of $20{\text{ms}}^{-1}$. A person standing outside on the ground also observes the ball. How will the maximum height $\left(h_m\right)$ attained and the ranges $\left(R\right)$ seen by the thrower and the outside observer compare each other?

• A. same $h_m$ different $R$
• B. same $h_m$ and $R$
• C. different $h_m$ same $R$
• D. different $h_m$ and $R$

Answer 1

The correct option is A same $h_m$ different $R$

The motion of the train will affect only the horizontal component of the velocity of the ball while the vertical component will remain same for the observer standing outside.
Since
Maximum height, $h_m=\frac{u^2{\sin }^2\theta }{2g}=\frac{u_y^2}{2g}$
Horizontal range, $R=\frac{u^2\sin 2\theta }{g}=\frac{2u_x{u}_y}{g}$
Since $u_y$ remains constant and $u_x$ varies, therefore $h_m$ will be same, but $R$ will be different.