A stone is dropped from a rising balloon at a height of 91.8 m above the ground and it reaches the ground in 6 s. What was the velocity of the balloon just at the moment when the stone was dropped?

A stone is dropped from a rising balloon at a height of 91.8 m above the ground and it reaches the ground in 6 s.

If the stone were dropped from a stationary balloon, the time t taken for it to reach the ground would have been given by 91.8 = (1/2)*9.8*t^2

=> t = sqrt (91.8/4.9)

=> t = 4.328 s

But the stone takes 6 s to reach the ground. If the upward velocity of the balloon in V.

91.8 = -V*6 + (1/2)*9.8*36

=> 6*V = -84.6

=> V = 14.1 m/s

The balloon is rising up at 14.1 m/s when the stone is dropped from it.