physics help please :)?

Question

A 20 g rifle bullet traveling 225 m/s buries itself in a 3.9 kg pendulum hanging on a 2.5 m long string, which makes the pendulum swing upward in an arc. Determine the horizontal component of the pendulum's displacement.
In meters

Answer 1

First, I will find the vertical displacement

initial v of the combined mass plus bullet
0.02*225=3.92*v
solve for v
v=1.148 m/s
the KE will be lost to PE as the pendulum rises
.5*m*v^2=m*g*h
solve for h
h=0.067 m
using Pythagorean on the triangle to find the horizontal displacement, x

(2.5-h)^2+x^2=2.5^2
solve for x
0.5756 m
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