The speed of a rifle bullet may be measured by means of a ballistic pendulum. The bullet, of known mass m and unknown speed V, embeds itself in a stationary wooden block of mass M, suspended as a pendulum of length L. This sets the block to swinging. The amplitude x of swing may be measured and, using conservation of energy, the velocity of the block immediately after impact may be found. Derive an expression for the speed of the bullet in terms of m, M, L, and x.

Answer 1

steps:
from the height of M, get max PE at x swinging on a arc of L, which will be equal to the initialKE of the block and bullet after impact.
then, knowing initial KE of M and m, compute velocity when they go up.
Now, considering conservation of momentum, determine initial velocity of m