Question

A 24g rifle bullet traveling 290m/s buries itself in a 4.0kg pendulum hanging on a 3.0m long string, which makes the pendulum swing upward in an arc.

Determine the vertical and horizontal components of the pendulum's displacement.

Express your answers using two significant figures. Enter your answers numerically separated by a comma.

Answer 1

Note that momentum must be conserved:

m1v1i + m2v2i = m1v1f + m2v2f

When they stick together, v1f = v2f = v. Thus,

v = 1.7296 m/s

Thus, the maximum height they reach is

h = v^2 /2g = 0.15 m   [ANSWER, vertical component]

Note that

h = R(1 - cos (A)), where R = length of the pendulum.

Thus,

A = 18.355 degrees

Thus, as displacement along x is

x = Rsin(A)

Then

x = 0.945 m    [ANSWER, horizontal component]

SUMMARY:

x = 0.94 m    [ANSWER, horizontal component]

h = y = v^2 /2g = 0.15 m   [ANSWER, vertical component]