Question

A simple pendulum is made from a 2 kg. block of wood suspended from a light cord of length 1 m. When the pendulum is hanging in such a way that it is stationary and vertical, a bullet is shot horizontally into the block of wood where it sticks. The bullet has a mass of 1.00 x 10^2 kg. and has a speed of 500 m/s just before its head-on collision with the block. What is the pendulum's maximum vertical angle as it swings?

Answer 1

I assume a typo and bullet is 10 grams

initial momentum of bullet and mass before collision

= 500 * 10^-2 kg + 0 * 2 kg = 5 kg m/s

the momentum just after collision will be the same with a mass now of 2.010 kg
and speed v
so
2.010 v = 5

calculate v from that

now the pendulum starts with speed v at the bottom
it has kinetic energy of
(1/2)(2.01) v^2

it slows to a stop as it rises
the rise distance is
1 meter (1 - cos T)
where T is the angle you want
the potential energy increase is
m g h = 2.01 * 9.81 * (1-cos T)
so in the end

1-cos T = (1/2) v^2/ [9.81]