How to find the initial speed of the bullet in this problem?

Question

A 7.0 g bullet is fired into a 1.5 kg ballistic pendulum. The bullet emerges from the block with a speed of 200 m/s, and the block rises to a maximum height of 12.5 cm. Find the initial speed of the bullet.
m/s

Answer 1

First, compute the speed of the pendulum after collision

.5*m*vi^2=m*g*h
vi=sqrt(2*g*h)
vi=sqrt(2*1.5*.125)
vi=0.61237 m/s

now we can relate this to the speed of the bullet using conservation of momentum

7.0*v0/1000=1.5*0.61237+7*200/1000
solve for v0
v0=331 m/s

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