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)`)

Answer

4

Explanation

Velocity attained by the baloon is 8x : v = u + at `rArr` v = 0 + 1.25 `xx` 8 = 10 m/s.
Above calculated velocity will be the initial velocity of the stone .
Displacement of balloon is 8 s:
`S = ut + (1)/(2) at^(2) =0 + (1)/(2) xx 1.25 xx (8)^(2) = 40 m` .
Now we can say that stone has initial velocity 10 m/s directed upwards and final displacement to reach the ground in 40 m downward. Acceleration due to gravity id always downwards.
Let us assume downward direction to be positive and using the following equation :
`S = ut = (1)/(2) at^(2)`
`rArr " "40 = - 10t + (1//2) xx 10 xx t^(2)`
`rArr " " 5t^(2) - 10t - 40 = 0`
`rArr " " t^(2) - 2t - 8 = 0` `rArr " " t = (2 pm sqrt(4 + 32))/(2) = (2 pm 6)/(2)`
Only positive sign will provied correct answer.
`rArr t = 4 s`
Hence answer is 4.