A balloon starts rising from the ground with an acceleration of 1.25 m/s2. After 8 s …

Q: A balloon starts rising from the ground with an acceleration of 1.25 m/s2. After 8 s, stone is released from the balloon. The stone will (g = 10 m/s2 )

(a) cover a distance of 40 m

(b) have a displacement of 50 m

(c) reach the ground in 4 s

(d) begin to move down after being released

Ans: (c)

Sol: Taking vertical upward motion of balloon for 8 sec.

v = u + a t

= 0 + 1.25 × 8

= 10 m/s

$ \displaystyle s = ut + \frac{1}{2}a t^2 $

$ \displaystyle s = 0 + \frac{1}{2}\times 1.25 \times 8^2 $

= 40 m

Taking vertical downward motion of stone released from balloon, we have

$ \displaystyle s = ut + \frac{1}{2}a t^2 $

$ \displaystyle 40 = -10 t + \frac{1}{2}(10) t^2 $

$ \displaystyle 5 t^2 -10 t -40 = 0 $

$ \displaystyle t^2 – 2 t – 8 = 0 $

On solving, t = 4 s