Question

A m2 = 6 kg block of clay is suspended from the ceiling by a long cord, as seen in the following figure. A m1 = 210 gram bullet, fired horizontally, imbeds itself into the clay, causing both masses to rise to a height of 4 m. What is the velocity of the bullet?

Answer #1

Gravitational acceleration = g = 9.81 m/s^{2}

Mass of the bullet = m_{1} = 210 g = 0.21 kg

Mass of the block of clay = m_{2} = 6 kg

Firing velocity of the bullet = V_{1}

Velocity of the bullet and the block of clay after the collision
= V_{2}

By conservation of linear momentum,

m_{1}V_{1} = (m_{1} +
m_{2})V_{2}

Height the both masses are raised to = H = 4 m

The kinetic energy of the block of clay and the bullet after the collision is converted into potential energy as they rise up.

(m_{1} + m_{2})V_{2}^{2}/2 =
(m_{1} + m_{2})gH

V_{2}^{2} = 2gH

V_{1} = 261.97 m/s

Velocity of the bullet = 261.97 m/s

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