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Forensic scientists can measure the muzzle velocity of a gun by firing a bullet horizontally into a large hanging block that absorbs the bullet and swings upward. (See the figure below.) The measured maximum angle of swing can be used to calculate the speed of the bullet. In one such test, a rifle fired a 4.20 g} bullet into a 2.50 kg} block hanging by a thin wire 75.0 cm} long, causing the block to swing upward to a maximum angle of 33.2 degrees from the vertical.

Forensic scientists can measure the muzzle velocity of a gun by firing a bullet horizontally into a large hanging block that absorbs the bullet and swings upwar class=

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Δh = 0,75*(1-cos32.2°) = 0.115 m 
V = √2gh = √19,6*0.115 = 1,50 m/sec 

applying momentum conservation principle : 
I = M*V = 2.504*1.50 = 3,76 kgm/sec 
3.76 = 0,0042*Vb 
Vb = 3.76/0.0042 = 895 m/sec
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Using the principle of conservation of momentum, the velocity of the fired bullet is 922.14 m/s

Given the Parameters :

  • Speed of bullet, V
  • Length of wire, L = 75.0 cm
  • L = 75/100 = 0.075 m
  • θ = 33.2°
  • Mass of bullet = 0.0042 kg

[tex] V = \sqrt{ [2gL(1 - cos \theta)]} [/tex]

[tex] V = \sqrt{ [2(9.8)(0.75)(1 - cos(33.5))]} = \sqrt {2.40} = 1.55 m/s [/tex]

Using the principle for the conservation of momentum :

  • Momentum, p = mass × velocity

Momentum of block = 2.5 × 1.55 = 3.873 Kgm/s

Momentum of block = momentum of bullet ;

Mass of bullet = 4.20 g = 4.20/1000 = 0.0042 kg

3.873 = (0.0042 × v)

v = 3.873 / 0.0042

v = 922.14 m/s

Therefore, the velocity of the bullet is 922.14 m/s

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