A bullet is fired into a huge wooden block. The bullet while moving inside the block loses halfthe velocity when it travels 3 cm inside the block. How far, then would it go inside the block ? Resistive force is constant.

Options

A. 1 cm
B. 2 cm
C. 3 cm
D. 4 cm

Answer

A

Explanation

From equation,
`v ^(2) - v _(0) ^(2) = 2ad`
`therefore a = (v ^(2) - v_(0) ^(2))/( 2d) = ((v _(0)/( 2))- v_(0) ^(2))/(2xx3)[because v = (v _(0))/(2) ]`
`therefore a =- (v _(0) ^(2))/(8)`
Now, for another distance, initial velocity is `(v _(0))/(2) ` and final velocity is zero.
`therefore d = (v ^(2) - v _(0) ^(2))/( 2a) = ((0)^(2) - ((v _(0))/( 2 )) ^(2) )/( 2 (- (v _(0) ^(2))/( 8 ))) = (- (v _(0) ^(2))/(4))/(- (v _(0) ^(2))/( 4)) =1 cm`