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

Explanation

Let `m` be the mass of bullet and `upsilon` be its initial velocity. If `F` is constant resistance to motion, then
`(i)` Work done `=` loss in KE `=` force `xx` distance
`=(1)/(2) m(upsilon^(2)-(upsilon^(2))/( 4))=Fxx3`
or `(1)/(2) m ( (3 upsilon^(2))/(4))=Fxxs ....(i)`
`(ii)` Work done `=` loss in KE `=` force `xx` distance
`=(1)/(2) m ( (upsilon^(2))/( 4)-0)=Fxxs...(ii)`
Dividing `(ii)` and `(i)`, we get
`(1)/(3) =(s)/(3)`
`:. s = 1 cm`