Question

A trolley having a cannon fixed to it which can shoot only vertically, is moving with a velocity $v_0=12\text{m/sec}$ in horizontal direction. At a certain instant, it is at a distance of $120\text{m}$ from a balloon which is held on ground and now it is released. The balloon starts rising with constant velocity $2v_0$. Calculate the minimum velocity(in $\text{m/s}$) of cannon ball so that it can hit the balloon.

Answer 1

Time taken by cannon ball covering distance $x$,
$t_0=\frac{x}{v_0}=\frac{120}{12}=10\text{sec}$
Height moved by balloon, $h=2v_0{t}_0=240\text{m}$
In time $t_0$, ball also moves a height $h$,

$h=v_y{t}_0-\frac{1}{2}g{t}_0^2$
$240=v_y\times 10-\frac{1}{2}\times 10\times 100$
$v_y=74\text{m/s}$