A bullet enters a block of wood with a velocity u. Its velocity decreases to v after going through a distance x inside. After covering a further distance y inside the bullet stops. Prove that `(u)/(v) =sqrt((y+x)/(y))`.

Explanation

Retardation of the bullet inside the block ,
a= constant
According to the equation `v^(2) = u^(2) -2as`
`v^(2)=u^(2)-2ax`
and 0 = `u^(2)-2a(x+y) " ""or", 2a = (u^(2))/(x+y)`
`:. " " v^(2) =u^(2) - (u^(2)x)/(x+y) = u^(2) (1-(x)/(x+y)) = (u^(2)y)/(x+y)`
or, `(u^(2))/(v^(2))= (x+y)/(y) " ""or",(u)/(v)= sqrt((y+x)/(y))`