A pendulum consists of a 1.7-kg block hanging on a 1.6-m length string. A 0.01-kg bullet moving with a horizontal velocity of 828 m/s strikes, passes through, and emerges from the block (initially at rest) with a horizontal velocity of 340 m/s. To what maximum height above its initial position will the block swing? Write your answer in meters.

0.42 m

Explanation:

mass of pendulum, M = 1.7 kg

Length of pendulum, l = 1.6 m

mass of bullet, m = 0.01 kg

initial velocity of bullet, u = 828 m/s

final velocity of bullet, v = 340 m/s

initial velocity of pendulum, U = 0

Let the final velocity of pendulum is V.

Use conservation of momentum for bullet and the pendulum

m x u + M x U = m x v + M x V

0.01 x 828 + 1.7 x 0 = 0.01 x 340 + 1.7 x V

8.28 + 0 = 3.4 = 1.7 V

V = 2.87 m/s

Now the kinetic energy of the pendulum is converted into potential energy of pendulum and let it raised to a height of h from the initial level.

Use energy conservation

Kinetic energy of the pendulum = potential energy of the pendulum

0.5 x M x V² = M x g x h

0.5 x 2.87 x 2.87 = 9.8 x h

h = 0.42 m