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A balloon starts rising from the ground ...

A balloon starts rising from the ground with a constant acceleration of `1.25m//s^(2)`. After 8 s, a stone is released from the balloon. Find the time taken by the stone to reach the ground. (Take `g=10m//s^(2)`)

A

cover a distance of 50 m till it strikes the ground.

B

have a displacement of 50 till it reaches the ground.

C

reach the ground in 4 seconds.

D

begin to move down instantaneously.

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
Height of balloon after 8 s:
`h_1=(1)/(2)xx(1.25)xx(8)^2=40`m
Velocity of balloon at this time:
`v_1=1.25xx8=10(m)/(s)`
Further height raised by stone:
`h_2=(v_1^2)/(2g)=(10^2)/(2xx10)=5` m
Distance covered by stone after is released:
`=AB+BC=5+45=50`m
and displacement `=AC=40`m
for stone: from A to C:
`-h_1=v_1t-(1)/(2)gt^2implies-40=10t05t^2`
`impliest^2-2t-8=0implies(t-4)(t+2)=0`
`impliest=4`s.
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