Question

A 16 g rifle bullet traveling 210 m/s buries itself in a 3.8 kg pendulum hanging on a 2.8 m long string, which makes the pendulum swing upward in an arc. Determine the horizontal component of the pendulum's displacement.

Answer 1

m₁ = mass of the bullet = 0.016 kg
m₂ = mass of the pendulum = 3.8 kg
v = speed of the bullet = 210 m/s
L = length of the pendulum = 2.8 m
g = acceleration by gravity = 9.8 m/s²

Dx = horizontal displacement = ?
Dy = vertical displacement = ?

The combined mass of the pendulum with bullet is:
M = m₁ + m₂ = 3.816 kg

The speed of the combined mass just after impact is:
V = m₁ v / M = 0.880 m/s

The maximum vertical displacement of the combined mass is:
Dy = V² / 2g = 0.0394 m

The maximum horizontal displacement of the combined mass is:
Dx = √(L² - (L - Dy)²) = 0.468 m