A 10-g bullet of unknown speed is shot horizontally into a 2-kg block of wood suspended from the ceiling by a cord. The bullet hits the block and becomes lodged in it. After the collision, the block and the bullet swing to a height 30cm above the original position. What was the speed of the bullet? (This device is called the ballistic pendulum). Take g=98ms−2

Hint: determine the KE that the block + imbedded bullet must have at the moment of impact in order to achieve a rise of 30cm against gravity. Then use conservation of momentum to determine the initial velocity of the bullet that matches the momentum needed for the block + bullet as it begins its movement.

Note that you can't simply equate the kinetic energy of the bullet to the rise in potential energy of the block + bullet, as energy is not conserved in an inelastic collision like this.