How high does the combined bullet and baseball rise after collision, assuming the ball and bullet are one?

Question

A 0.30-kg bullet is fired vertically at 200 m/s into a .15-kg baseball that is initially at rest. Please show work using the conservation of momentum and conservation of energy.

Answer 1

Finding the velocity of ball+bullet is a momentum problem:
m1v1+m2v2 = (m1+m2)v3
v3 = (m1v1+m2v2)/(m1+m2)
v2 = 0, so v3 = m1v1/(m1+m2)
Conservation of energy says KE1+KE2 = PE1+PE2
In this case PE1 = KE2 = 0, so PE2 = KE1, thus
mgh = mv^2/2; h = v^2/(2g)
Height reached h = v3^2/(2g)