find total energy and initial velocity of the bullet?

Question

Assume: The bullet penetrates into the block and stops due to its friction with the block. The compound system of the block plus the bullet rises to a height of 10 cm along a circular arc with a 18 cm radius.

Assume: The entire track is frictionless. A bullet with a m1 = 30 g mass is fired horizontally into a block of wood with m2 =
4.8 kg mass.

The acceleration of gravity is 9.8 m/s^2.

Calculate the total energy of the composite system at any time after the collision. Answer in units of J.

Taking the same parameter values as those in Part 1, determine the initial velocity of the bullet. Answer in units of m/s.

Answer 1

The total energy after collision can be calculated by considering the potential energy gained in the height gained up the circular arc
(m1+m2)*g*h
(.03+4.8)*9.8*.1
=4.7334 J


Part 2
using the energy equatin the kinetic energy after collision is
.5*(m1+m2)*v2^2
so v2=sqrt(2*g*h)

using conervation of momentum for the inelastic collision of the bullet and the block
m1*v1=(m1+m2)*v2
v1=(m1+m2)*sqrt(2*g*h)/m1
v1=(4.8+.03)*
sqrt(2*9.8*.1)/.03


v1=225 m/s

j