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 0.009 kg, and its velocity is +738 m/s. Her mass (including the gun) is 52 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?
1 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 multiplied by 10-4 kg at a velocity of +738 m/s?
2 m/s

Explanation / Answer

we have,
Mass of bullet m = 0.009 kg
speed of bullet = 723 m/s
Mass of lady = 47 kg
from Conservation of momentum,

mu1 + Mu2 = mv1 + Mv2
0 + 0 = 0.009 x 723 + 47 x v2
v2 = -0.138 m/s

Recoil velocity = -0.138 m/s
( negative sign denotes the direction is opposite to bullet)

b. for second part,
from Conservation of momentum,

mu1 + Mu2 = mv1 + Mv2
0 + 0 = 5.0x10-4x 723 + 47 x v2
v2 = -0.00769 m/s

Recoil velocity = -0.00769 m/s

( negative sign denotes the direction is opposite to bullet)

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