A bullet of mass ‘m’ traveling horizontally at a speed ‘v’ embeds itself in the centre of a block of wood of mass ‘M’, which is suspended by a light vertical string of length ‘l’. What would be the maximum inclination of the string with the vertical?

Answer 1

After the bullet gets embedded in the block, the block acquires velocity V given by

mv = (m+M) V
V = [m/(m+M)] v

Then the pendulum swings to a height H while total energy is conserved:

gH = V^2/2 = [m/(m+M)]^2 v^2/2

If the maximum inclination angle of the swing is A and the string length is l,

l (1 - cos A) = H

Solve for A