A bullet having a speed of `100 m//see` crashes through a plank of wood. After passing through a plank , its speed is `80 m//s`. Another bullet of the same mass and size , but traveling at `80 m//s` is fired at the plank . The speed of the second bullet after traveling through the plank is (Assume that resistance of the plank is independent of the speed of the bullet) :

Options

A. `10 sqrt(7) ms^(-1)`
B. `20 sqrt(7) ms^(-1)`
C. `30 sqrt(7) ms^(-1)`
D. `20 sqrt(7) ms^(-1)`

Explanation

Suppose `F` be the resistance force offered by the plank . Let thickness of plank be `x`.
For first case: `Fx = (1)/(2) m [(100)^(2) - (80)^(2)]` (i)
For second case, let `V` be the final velocity of bullet, then `Fx = (1)/(2) m [(80)^(2) - V^(2)]` (ii)
From (i) and (ii) `80^(2) - V^(2) = 100^(2) - 80^(2)`
or `V = 20 sqrt(7) m//s`