Question

a bullet fired into a target loses 1/n th of its velocity after penetrating a distance x into the target how far the will it penetrate before it comes to rest express your answer in terms of n and x

Answer 1

$(\frac{n-1}n v)^2=v^2-2ax,$ $\implies$

$2a=\frac{2n-1}{n^2}\frac{v^2}x,$

$(\frac{n-1}n v)^2=0^2+2al,$

$l=(\frac{n-1}n v)^2\cdot \frac{n^2}{2n-1}\frac x{v^2}=x\frac{(n-1)^2}{2n-1}.$