A balloon starts rising from ground with an acceleration of 1.25 m$/{\sec }^2$. After 8 seconds a stone is released from the balloon. The maximum height from the ground reached by stone will be

When a particle separates from a moving body it retains the velocity of the body but not its acceleration.

 At the instant of released the balloon is s = $\frac{1}{2}\times (1.25)\times 64 = 40 \mathrm{m} \mathrm{above} \mathrm{the} \mathrm{ground} \mathrm{and} \mathrm{is} \mathrm{having} \mathrm{an} \mathrm{upward} \mathrm{velocity} = 1.25\times 8 = 10 \mathrm{m}/\sec .$

For the motion of the stone from the balloon, a = -g = -10 $\mathrm{m}/{\mathrm{s}}^2$

v = 0 using ${\mathrm{v}}^2-{\mathrm{u}}^2 = 2\mathrm{as}$

0-100 = -2 $\times$10$\times$s

s = 5 metres

$\therefore$maximum height from ground = 40+5 = 45 m