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 +736 m/s. Her mass (including the gun) is 46 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 10-4 kg at a velocity of +736 m/s?

Explanation / Answer

Given that
mass of bullet m = 0.005 kg
speed of the bullet is u = + 736 m/s
Her mass (including the gun) is M = 46 kg
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a) FRom the law conservation of momentum
Initial momentum =Final momentum
0 = mu + Mv
v = -(mu)/M
=- (m/M)u
= - (0.005 kg/46kg)(736 m/s)
=-0.08 m/s

b) From the law of conservation of momentum
v= - (mu)/M
Here m = 5.0x10^-4 kg
u = 736 m/s
M = 46 kg

v = - (mu)/M
=- (m/M)u
= - (( 5.0x10^-4 kg )/(46kg))(715 m/s)
=- 0.008 m/s

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