A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm . How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?

Options

A. 1.5 cm
B. 1.0 cm
C. 3.0 cm
D. 2.0 cm

Answer

B

Explanation

u = Initial velocity
After 3 cm , it velocity = `u/2 `
`v^(2)-u^(2)-2as`
`rArr (u^(2))/4 =u^(2) - 2axx3 rArr 6a = (3u^(2))/4 rArra = (u^(2))/8`
Let it will penetrate further x distance
v = 0 , `u= u/2 , a= (u^(2))/8`
`v^(2) =u^(2) -2as`
`rArr 0 = (u^(2))/4 - 2 xx (u^(2))/8 xx x `
`rArr (u^(2))/4 x = (u^(2))/4 rArr x = 1 `cm .