Liam fires a bullet into a block suspended by two cables, embedding the bullet in the block. The mass of the bullet is 5g and the mass of the block is 1g.

Question

1) If the maximum height of the block is ,h, is 35 cm, how fast was the bullet originally moving?

(can you explain the steps i'm really confused)

Answer 1

m1= mass of the bullet
m2= mass of the block
Vf=sqrt(2gh)
v1= initial velocity of bullet
v2= initial velocity of the block = 0

so
first is conservation of momentum
m1v1+m2v2=(m1+v2)Vf
solve for v1 (note m2v2=0)
v1=((m1+m2)/m2)/Vf
to find Vf look at conservation of energy
KE+PE=KE'+PE'
.5(m1+m2)Vf^2+0=0+(m1+m2)gh
Solve for Vf and you get Vf=Sqrt(2gh)
now v1=((m1+m2)/m2)/(sqrt(2gh)) and solve
v1= 15.715 m/s