Question

The lead female character in the movie Diamonds Are Forever is standing at the edge of an offshore oil rig. As she fires the gun, she is driven back over the edge and into the sea. Suppose the mass of a bullet is 0.005 kg, and its velocity is +713 m/s. Her mass (including the gun) is 53 kg.

(a) What recoil velocity does she acquire in response to a single shot from a stationary position, assuming that no external force keeps her in place?

(b) Under the same assumption, what would be her recoil velocity if, instead, she shoots a blank cartridge that ejects a mass of 5.0 multiplied by 10-4The lead female character in the movie Diamonds Are Forever is standing at the edge of an offshore oil rig. As she fires the gun, she is driven back over the edge and into the sea. Suppose the mass of a bullet is 0.005 kg, and its velocity is +713 m/s. Her mass (including the gun) is 53 kg.

(a) What recoil velocity does she acquire in response to a single shot from a stationary position, assuming that no external force keeps her in place?

(b) Under the same assumption, what would be her recoil velocity if, instead, she shoots a blank cartridge that ejects a mass of 5.0 multiplied by 10-4

Answer 1

For this question you need to apply the law of conservation of momentum. Initially the entire system has 0 momentum since both herself and the bullet are at rest (V=0). After she fires the gun, the bullet does not have zero momentum, since Vbullet is 713 m/s. So:

\[\Sigma p_{initial} = \Sigma p_{final}\]\[p_{female initial} + p_{bullet initial} = p_{female final} + p_{bullet final}\]\[0 = m_{bullet}V{bullet} + m_{female}v_{female}\]Rearranging this for the velocity of the bullet gives us
\[\frac{-m_{bullet}v_{bullet}}{m_{female}}\] which, when you plug in your values should give you: \[V_{female} = - 0.0673 m/s\]

in part b, you're not given a velocity for the blank, so I suppose we should just assume it's travelling at the same velocity as the bullet. In this case we just take our equation in which we've already solved for the velocity of the female character and plug in new values, This should give us: \[v_{female} = - 0.00673 m/s \]