From ground a balloon starts ascending at a constant speed of 25 m/s. After 5 sec a bullet is shot vertically upward from the ground. Find the minimum speed of bullet at which it is able to hit the balloon.

Analyzing motion of bullet

w.r.t balloon we use

${\mathrm{v}}_{\mathrm{BB}}=\mathrm{u}-25$

$\text{ acc of bullet }\mathrm{a}=-\mathrm{g}=-10 \mathrm{m}/{\mathrm{s}}^2$

when bullet is fired at t = 5 s, the balloon is at a height of h = vt = 25x5 = 125 m

u should be such that it will reach to a minimum height of 125 m

$\Rightarrow 125=\frac{(\mathrm{u}-25{)}^2}{2\mathrm{g}}\Rightarrow \mathrm{u}-25=\sqrt{125\times 2\times 10}=50$ m/s

                                         $\text{u=75 m/s}$