A stone is dropped from the top of tower. If its velocity at the mid point of height of tower is `10ms^(-1),` then the height of a tower is ..... `(g = 10 ms^(-2))`

Options

A. 10
B. 16
C. 8
D. 20

Answer

A

Explanation

Suppose initial speed of ball is `v _(0)` and maximum height is h.
Now, for first half distance `d = (h)/(2)`
`2ad =v ^(2) -v _(0) ^(2)`
`2 xx (-10 ) h/2 = (10) ^(2) - v _(0) ^(2)`
`therefore -10 h = 100 -v_(0) ^(2)`
`therefore - 10h -100 =- v_(0) ^(2) " "...(1)`
Now for maximum height `d = h, v _(0) = v _(0), v =0,`
`a = 10 ms ^(-2)`
`therefore 2ad =v ^(2) -v_(0) ^(2)`
`therefore - 2 xx 10 xx h = 0- v _(0) ^(2) `
`therefore -20h =-v _(0) ^(2) " "...(2)`
From equation (1) and (2),
`-20 h =- 10h -100`
`therefore -10 h =-100`
`therefore h = 10m`