"Forensic scientists can measure the muzzle velocity of a gun by firing a bullet horizontally into a large hanging block that absorbs the bllet and swings upward. The measured maximum angle of swing can be used to calculate the speed of the bullet. In one such test, a rifle fired a 4.20g (.0042kg) into a 2.50 kg block hanging by a thin wire 75.0cm (.75m), causing the block to swing upward to a maximum angle of 31.2degrees from the vertical."

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Solution lies in Conservation of Energy

In this case Kinetic Energy of bullet increases Potential Energy of Block.

Let mass of bullet be m1, mass of block m2, length of wire L

(I assume we neglect length of block)

Let angle of swing be A

Hence block rises (L - L cos A) vertically

Let velocity of bullet be V

Initially Kinetic energy of bullet = 1/2 m1 V^2

Finally, Energy Change

= Increase in potential energy of block

= mass times gravity times height

= m2 g (L - Lcos A)

Hence

1/2 m1 V^2 = m2 g (L - Lcos A)

Substitute values of m1, m2, L, A, g to get value of V