How Can You Simplify This Math Homework Equation?

AI Thread Summary
To simplify the equation (mBvB2 - mBvC2 - mCvC2)/(mBvB2) to mC/(mC + mB), additional relationships between the variables are necessary, as the current variables are not adequately defined. The discussion highlights that if vB equals vC, the left side simplifies to -mC/mB, which only matches the right side under specific conditions. Participants suggest canceling unnecessary variables like gravitational acceleration (g) and height (h) to aid in simplification. Ultimately, the need for more contextual information about the variables is emphasized to achieve the desired simplification. The conversation underscores the importance of clearly defined variables in mathematical equations.
gold123456th
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Homework Statement


Show how to simplify (mBvB2 - mBvC2 - mCvC2)/(mBvB2) to mC/(mC + mB)


Homework Equations


vB is not equal to vC.
vB = muzzle speed of a bullet = unknown value
vC = speed of the clay block after it is hit by the bullet = unknown value
vB = ((2gh)0.5(mB + mC))/mB
vC = (2gh)0.5
g = gravitational acceleration
h = unkown height
mB is not equal to mC
mB is the mass of a bullet. mB is unkown though
mC is the mass of a clay block. mC 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!
 
Last edited:
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gold123456th said:

Homework Statement


Show how to simplify (mBvB2 - mBvC2 - mCvC2)/(mBvB2) to mC/(mC + mB)

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 vB = vC. In this case the equation on the left reduces to -mC/mB, which is only matches the right hand side when mC = 0 or mC = -2mB.

So you need more information.

Cheers -- sylas
 


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


gold123456th said:
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?
 


Yeah of course
 
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