Question

DPPS BOOKLET-1
A balloon is moving with constant upward acceleration of 1 m/s2. A
stone is thrown from the balloon downwards with speed 10 m/s with
respect to the balloon. At the time of projection balloon is at height 120 m
from the ground and is moving with speed 20 m/s. The time required by
the stone to fall on the ground after the projection will be - (g = 10 m/s)
(A) 4 sec.
(B) 5 sec
(C) 6 sec.
(D) None of these​

Answer 1

Answer:

The time required is 6 sec . The correct answer is option C

Explanation:

According to the problem the acceleration of the balloon is 1 m/s^2

Now the velocity of the stone is thrown be u m/s  

According to the problem the  velocity  of the balloon with respect to balloon in upwards is  20 m/s will be = u + 20.

According to the problem it is given as 10 m/s

Therefore, u = -10 m/s

Now at the time of projection the height of the balloon from the ground is h= 120 m

Now, h = ut + 1/2 g t^2,

=> -120 = 10t - 1/2 x 10  t^2

=> -120 = 10t - 5  t^2

=>  t^2 -2t - 24 = 0  

(t-6)(t+4) = 0

Hence  t = 6 s