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 0.006 kg, and its velocity is +734 m/s. Her mass (including the gun) is 55 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? 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 +734 m/s? m/s

Explanation / Answer

a)

m = mass of bullet = 0.006 kg

v = velocity of bullet = 734 m/s

M = mass of person + gun = 55 kg

V = recoil velocity

Using conservation of momentum

initial momentum before fire = final momentum just after bullet is fired

Pi = Pf

0 = mv + M V

- 0.006 x 734 / 55 = V

V = - 0.08 m/s

in opposite direction of bullet

b)

m = mass of cartridge = 5 x 10-4 kg

v = velocity of cartridge = 734 m/s

M = mass of person + gun = 55 kg

V = recoil velocity

Using conservation of momentum

initial momentum before fire = final momentum just after cartridge is fired

Pi = Pf

0 = mv + M V

- (5 x 10-4) x 734 / 55 = V

V = - 0.00667 m/s

in Opposite direction

V = - 0.08 m/s

in opposite direction of bullet

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