A bullet mass m1 is fired with a speed V into the wooden bob of a pendulum having mass m2.

the bob is attached to a very light ridiged rod of length L that is pivoted at the other end. the bullet is stopped in the bob. how high is the bob raised

initial KE = 0.5 m1 * V^2
moment of inertia M o I of pendulum after impact
= (m1 + m2) L^2
KE of pendulum combo
= 0.5 * M o I * w^2
initial momentum = m1 V
final momentum after impact = (m1 + m2) u
(m1 + m2) u = m1 V
u = m1 V / (m1 + m2)
= Lw
w = m1 V / [L* (m1 + m2)]
KE of pendulum combo
= 0.5 * M o I * w^2
= 0.5 * (m1 + m2) L^2 * [m1 V]^2 / [L* (m1 + m2)]^2
= final PE
= (m1 + m2) g * h

(m1 + m2) g * h = 0.5 * (m1 + m2) L^2 * [m1 V]^2 / [L* (m1 + m2)]^2
g * h = 0.5 * L^2 * [m1 V]^2 / [L* (m1 + m2)]^2
h = 0.5 * L^2 * [m1 V]^2 /g [L* (m1 + m2)]^2
h = 0.5 * [m1 V]^2 /g (m1 + m2)^2
h = 0.05 * [m1 V]^2 / (m1 + m2)^2
answer
high the combo bob raised