Calculating % Kinetic Energy Conversion in Ballistic Pendulum

[gold123456th]

Homework Statement

A soft clay block is suspended so as to form a so-called ballistic pendulum. A bullet is fired point-blank into the block, imbedding itself therein and raising the latter to a height h. Derive an expression for the percentage of the kinetic energy converted into internal energy during the bullet-clay impact.

Homework Equations

Use any equation related to momentum and kinetic energy

The Attempt at a Solution

I managed to get an expression: (m_Bv_B² - m_Bv_C² - m_CV_C²)/(m_Bv_B²) x 100
This expression is right, but I need to simplify it to (m_C)/(m_C + m_B) x 100. I don't know how to simplify this equation
Thanks!

 

[rl.bhat]

Use conservation of momentum and write VB in terms of VC. Substitute this in the energy equation to eliminate VC.

 

[gold123456th]

Can you show me how to do that? I tried but had no luck

 

[rl.bhat]

Can you show me how to do that? I tried but had no luck

m_BV_B = (m_B+m_C)V_C
Now what is VB ?

 

[gold123456th]

i got it! thanks