Question

A bullet can go through a block of 1 centimetre by what factor should it be increased so that it goes through four such blocks

Answer 1

If we assume that kinetic energy of the bullet fully converts into energy $E_b$ required to go trough a block, for one block the situation will look like

$$\frac{mv^2}{2}=E_b.$$

For 4 blocks, the equation is

$$\frac{mu^2}{2}=4E_b,\\\space\\ u=\sqrt{\frac{8E_b}{m}}=\sqrt{\frac{8(mv^2/2)}{m}}=2v.$$

To go through 4 blocks, the speed can be increased by a factor of 2.