Question

A rubber ball escapes from the horizontal roof with a velocity $v=5m{s}^{-1}$. The roof is situated at a height, h= 20 m. If the length of each car is equal to $x_0$ = 4 m, with which car will the ball hit?

Answer 1

The initial velocity of the ball is in horizontal direction. The initial velocity in vertical direction is zero.
For vertical motion, $u_x=5m{s}^{-1},u_y=0$
Displacement in vertical direction, $y=-h=-20m$
$-h=\frac{1}{2}-g{t}^2\Rightarrow \frac{2\times 20}{10}=t^2\Rightarrow t=2s$
Horizontal displacement: Distance covered in 2 s,
$x=d=u_x\times t=5\times 2=10m$
Since the length of one car is $4$ in, it will hit the third car for which $8m<d<12m.$