A person throws balls upward in regular intervals of time of 2 s. What should be the speed of throwing of balls such that both balls remain in air ?

Options

A. less than `19.6 ms ^(-1)`
B. equal to `19.6ms^(-1)`
C. less than `9.8ms ^(-1)`
D. greater than `19.6ms^(-1)`

Answer

D

Explanation

`f = f _(0) [1- (t)/(T)]`
`f = 0 because f _(0) [1 + (t)/(T)] =0`
`implies t = T`
Now `f = (dV)/(dt)`
`therefore (dV)/(dt) = f _(0) [1 - (t)/(T)]`
`int _(0) ^(V _(x)) dV = int _(t =0) ^(t =T) f _(0) [1- (t)/(T)]dt`
`v _(x) = f _(0) [t - (t ^(2))/(2T) ] _(0) ^(T) `
`V_(x) = f_(0) [T- (T ^(2))/(2T)]`
`V_(x) = f _(0) [T- (T)/(2)]`
`V_(x) = 1/2 f_(0)T`