Physics- Ballistic pendulum

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?

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  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]

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