Question

a balloon starts rising from the ground with an acceleration of 1.25m/s^2.A stone is released from the balloon after 10s.Determine the maximum height of stone from ground

Answer 1

After 8s the upward velocity of the balloon is =( according to u+at) (1.25)(8)=10 m/s.

Therefore, the stone will have initial upward velocity ,

u= 10 m/s………..(1)

We have taken upward direction as positive.

The acceleration of the stone, after it is realesed is

g=- 9.8 m/s^2………..(2)

The height of the balloon at 8s is ,

h=(1/2)at^2=(1/2)(1.25)(64)=40m.

Now, using h=ut+(1/2)gt^2, we have

-40=10t- (1/2)(9.8)t^2. Therefore,

4.9t^2–10t-40=0. The roots of this quadratic equation are

t={10+_ sqrt[100+(4)(4.9)(40)]}/9.8

t={10+sqrt[884]}9.8

t=(10/9.8)+3.03= 4.05s.