How Can You Simplify This Math Homework Equation?

[gold123456th]

Homework Statement

Show how to simplify (m_Bv_B² - m_Bv_C² - m_Cv_C²)/(m_Bv_B²) to m_C/(m_C + m_B)

Homework Equations

v_B is not equal to v_C.
v_B = muzzle speed of a bullet = unknown value
v_C = speed of the clay block after it is hit by the bullet = unknown value
v_B = ((2gh)^0.5(m_B + m_C))/m_B
v_C = (2gh)^0.5
g = gravitational acceleration
h = unkown height
m_B is not equal to m_C
m_B is the mass of a bullet. m_B is unkown though
m_C is the mass of a clay block. m_C is also unkown

The Attempt at a Solution

I have tried many different methods, but I still cannot show how to simplify the above equation
Please Help!

 

[sylas]

Homework Statement

Show how to simplify (m_Bv_B² - m_Bv_C² - m_Cv_C²)/(m_Bv_B²) to m_C/(m_C + m_B)

Homework Equations

The Attempt at a Solution

I have tried many different methods, but I still cannot show how to simplify the above equation
Please Help!

You need more equations showing some relationships between your variables. If the variables are uninterpreted, the equation doesn't hold. For example, suppose v_B = v_C. In this case the equation on the left reduces to -m_C/m_B, which is only matches the right hand side when m_C = 0 or m_C = -2m_B.

So you need more information.

Cheers -- sylas

 

[gold123456th]

I just edited the thread. Hope all the info are there

 

[sylas]

I just edited the thread. Hope all the info are there

Yes. Can you cancel out the variables you don't need? That is, g and h?

 

[gold123456th]

Yeah of course