A bullet with an initial velocity u penetrates a target. After penetrating a distance x, its velocity decreases by `(u)/(n)`. How much farther will the buIIet move through the before if comes to rest?

Explanation

Let us assume that the retardation of the bullet inside the target is a and it is iniform. After penetrating a distance x the velocity,
`v = u-(u)/(n) = (u(n-t))/(n)`
`:. "From"" " v^(2) = u^(2)-2`as, we get,
`(u^(2)(n-1)^(2))/(n^(2))=u^(2)-2`ax
or,`" " 2ax = u^(2)-(u^(2)(n-1)^(2))/(n^(2))`
=`u^(2)(1-(n^(2)-2n+1)/(n^(2)))=u^(2).(2n-1)/(n^(2))`
or, `" "a = (u^(2)(2n-1))/(2xn^(2))`
Let the bullet travel an additional distance y before it comes to rest.
`:." "(0)^(2) = u^(2)-2a(x+y)" "or, x+y = (u^(2))/(2a)`
or,`" "y = (u^(2))/(2a)-x = (u^(2).2xn^(2))/(2u^(2)(2n-1))-x=(xn^(2))/(2n-1)-x`
=`x((n^(2)-2n+1)/(2n-1)) = (x(n-1)^(2))/(2n-1)`.