The lead female character in the movie Diamonds Are Forever is standing at the e

Question

The lead female character in the movie Diamonds Are Forever is standing at the edge of an offshore oil rig. As she fires a gun, she is driven back over the edge and into the sea. Suppose the mass of a bullet is 0.0191 kg and its velocity is +890 m/s. Her mass (including the gun) is 51.4 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 0.000672 kg at a velocity of +890 m/s?

Explanation / Answer

This question is all about momentum. Since she is not moving at the start of the event, the total momentum of the system in each scenario must be 0 at all times. Thus, the momentum of the bullet is equal in magnitude to her momentum. The relevant equation is: p (momentum) = m (mass) * v (velocity) In the first case, m(bullet)*v(bullet) = -m(woman) * v (woman), where the negative sign only means that the woman travels in the opposite direction as the bullet. So, v(woman) = m(bullet)v(bullet)/m(woman) v(woman) = 0.0191 kg * 890 m/s / 51.4 kg = 0.331 m/s. In the second case, the equation is the same, but we use the smaller mass of the blank: v(woman) = m(blank)v(blank)/m(woman) = 0.000672 * 890 / 51.4 = 2.26 * 10^-4 m/s. As expected, the woman recoils with reduced velocity when the mass of the projectile is reduced.

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