Forensic scientists can measure the muzzle velocity of a gun by firing a bullet

Question

Forensic scientists can measure the muzzle velocity of a gun by firing a bullet horizontally into a large hanging block that absorbs the bullet and swings upward. (See the figure below.) The measured maximum angle of swing can be used to calculate the speed of the bullet. In one such test, a rifle fired a 4.20 g bullet into a 2.50 g block hanging by a thin wire 75.0 cm long, causing the block to swing upward to a maximum angle of 30.2 degrees from the vertical.

What was the original speed of this bullet?

Explanation / Answer

Conservation of momentum... m1*u1 + m2*u2 = mf*vf where m1 and m2 are the two masses, mf is the final mass (m1+m2) u1 and u2 are the initial velocities vf is the final velocity bullet mass (in kg) * initial velocity + wood mass * initial velocity = final mass * final velocity (About 3 times the speed of sound, a little on the high side for a bullet but possible)

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