To what depth will the bullet penetrate the block in this case?

Question

A 7.00 g bullet, when fired from a gun into a 1.00 kg block of wood held in a vise, penetrates the block to a depth of 8.00 cm. This block of wood is next placed on a frictionless horizontal surface, and a second 7.00-g bullet is fired from the gun into the block. To what depth will the bullet penetrate the block in this case?

Answer 1

7 ∆vi^2 = 8k
7vi = 1007vf
vf = 7vi/1007
∆v = vi(1 - 7/1007) = 1000vi/1007
∆v^2 = (1000vi/1007)^2
1/8 = (1000/1007)^2/x
x = 8(1000/1007)^2 = 7.8892 cm