Question

A balloon starts rising from the ground with acceleration of 1.25 m/s2. After 8 s a stone is released from the balloon. how much time will it take to reach the ground

Answer 1

Final Answer : 4 s

Steps:
1) Initially,
Initial velocity, u = 0m/s
acceleration, a =1.25 m/s^2
Velocity of balloon after 8 s, v = u +at
=> v = 0 + 1.25 * 8 = 10m/s

2) Displacement of balloon in 8 s,
$s = ut + \frac{1}{2} a {t}^{2} \\ = > 0 + \frac{1}{2} \times 1.25 \times {8}^{2} = 40m$

3) After t = 8s, a stone is dropped.
Initial velocity of stone at time of fall is same as that of balloon at that time :
That is velocity of stone,when it is dropped is 10m/s upward.

Initial velocity, u = 10m/s
Displacement, s = -40m ( - means downward)
Balloon is left.
Acceleration, a = -10 m/s^2


So, time taken by stone to reach the
$s = ut + \frac{1}{2} a {t}^{2} \\ - 40 = 10t + \frac{1}{2} \times( - 10) \times {t}^{2} \\ = > {t}^{2} - 2t - 8 = 0 \\ = > (t + 2)(t - 4) = 0$
t = 4 s, t = -2 (rejected)

Therefore, Stone will take 4 seconds to reach the ground after being dropped from balloon at height h =40m from ground.

Answer 2

Answer:

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