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 0.005 kg, and its velocity is +732 m/s. Her mass (including the gun) is 56 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? in m/s

(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 10-4 kg at a velocity of +732 m/s? in m/s

Explanation / Answer

Given,

m = 0.005 kg ; v = 732 m/s ; M = 56 kg

a)Let V be her recoil velocity.

From conservation of momentum:

Pi = Pf

0 + m v = M V

V = m v / M = 0.005 x 732 / 56 = 0.065 m/s

Hence V = 0.065 m/s (in opposite direction)

b) m = 5 x 10-4 = 0.0005 kg

V' = m v / M = 0.0005 x 732 / 56 = 0.0065 m/s

Hence V' = 0.0065 m/s (in opposite direction)

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