Question

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 (Figure 1).) 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 kgblock hanging by a thin wire 75.0 cm long, causing the block to swing upward to a maximum angle of 32.5 ∘ from the vertical.

Answer 1

Given,

Mass of the bullet, m = 0.0042 kg

Mass of the block, M = 2.5 kg

Length, L = 0.75 m

Angle, theta = 32.5 degree

Vertical height raised, h = 0.75 (1 - cos32.5) = 0.117 m

Using law of conservation of energy,   

0.5 (M + m) V^2 = (M + m) g h

V^2 = 2 g h

V = sqrt ( 2 x 9.8 x 0.117 ) = 1.52 m/s

From law of conservation of momentum,

m U = (m + M) V

Velocity, U = 2.5042 x 1.52 / 0.0042 = 904.66 m/s

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