Question

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

• A. 40 m
• B. 50 m
• C. 45 m
• D. 55 m

Answer 1

Answer: (C)

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
$s = \frac{1}{2} \times (1.25) \times 64 = 40\,m$
above the ground and is having an upward velocity
$= 1.25 \times 8 = 10 \,m/ \sec$.
For the motion of stone from the balloon to the highest point,
$u = 10\,m/s$.
$a = - g = - 10\,m/s^2$
$v = 0$ using $v^2 - u^2 = 2as$
$0 - 100 = -2 \times 10 \times s$
$s = 5$ metres
$\therefore $ maximum height from ground
$= 40 + 5 = 45 \,m $