Question

A 19 g rifle bullet traveling 230 m/s buries itself in a 3.1 kg pendulum hanging on a 2.8 m long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum's displacement.

vertical______	m
horizontal	_____m

Answer 1

Momentum of rifle and pendulum before impact = momentum of both after impact:

0.019*230 + 0 = (3.1 + 0.019)*v,

where v= velocity of both bullet and pendulum after impact.

v = 0.019*230/3.119 m/s = 1.401 m/s

Kinetic energy of system after impact = 1/2*m*v*v = potential energy = m *g*h, where h = height system rises after impact.

h = v*v/(2*g) = 1.401*1.401/2*9.81 = 0.100m = 10 cm = vertical displacement of pendulum.

(The horizontal displacement) ^2 = 2Lh - (h*h) = 2*2.8*0.100-(0.100)^2 = 0.55

The horizontal displacement = 0.7416 m