Question

A balistic pendulum is made from a block of wood with a mass of 2.78 kg. A bullet with a mass of 39 g is shot into the block causing it to rise 29.1 cm. What was the speed of the bullet?

Answer 1

find the speed of the pendulum at the bottom

mgh=1/2 m vi^2

now, knowing vi, from conservation
(Mb+mblock)vi=Mb*V

solve for the speed of the bullet V

Answer 2

momentum before = momentum just after
Vb bullet
v block and bullet

.039 Vb = (2.78+.039)v = 2.82 v

now work on potential and kinetic energy after
kinetic just after = .5 * 2.82 v^2
potential when stopped at top = m g h =2.82 * 9.81 * .291 = 8.05 Joules
so
1.41 v^2 = 8.05
v = 2.39 m/s
now back to that initial momentum equation
.039 Vb = 2.82 (2.39)
Vb = 173 m/s