A piece of stone was dropped from a stationary baloon. The stone covered 13.9 m during the last `(1)/(7)`s of its descent. Find the height of the balloon and the velocity of the stone whe it strikes the ground. [g = 9.8 `"m.s" ^(-2)`]

Explanation

Let h = height of the balloon t = total time of fall of the stone ,h. = downward displacement in time `(t-(1)/(7))`s.
Hence h-h. = `(1)/(2) "gt"^(2) - (1)/(2) g (t- (1)/(7))^(2)`
or,`" " 13.9 = (1)/(2) xx 9.8 xx t^(2) - (1)/(2) xx 9.8 (t-(1)/(7))^(2)`
or,`" " 13.9 = 4.9t^(2) - 4.9t^(2) +1.4 t-0.1`
or,`" " 1.4t = 14" ""or", t = 10`
`:.` Height of the balloon,
`h = (1)/(2) "gt"^(2) = (1)/ (2) xx 9.8 xx (10)^(2) = 490 `m
Velocity of the stone when it strikes the ground is ,
v = u +gt = 0 +`9.8 xx10 = 98 "m.s"^(-1).`