417,903 views
28 votes
28 votes
PLS I NEED HELP!!! :(((

M*V^2 = m*v^2
Solve for V.
Please show process.
a.) V = √(mv^2/M)
b.) V = mv^2/M
c.) V = v √(M/m)
d.) V = mv/M

User Bunnie
by
2.4k points

1 Answer

20 votes
20 votes

Answer:

a.) V = √(mv²/M)

Explanation:

As with any "solve for ..." situation, you make use of inverse operations to "undo" what is done to the variable of interest.

Solve

In the given equation ...

MV² = mv²

the variable V is squared and that result is multiplied by M. These operations are dealt with in reverse order.

To undo multiplication by M, we divide both sides of the equation by M.


MV^2=mv^2\qquad\text{given}\\\\(MV^2)/(M)=(mv^2)/(M)\qquad\text{divide by $M$}\\\\V^2=(mv^2)/(M)\qquad\text{simplify}

To undo the squaring of V, we take the square root.


√(V^2)=\sqrt{(mv^2)/(M)}\qquad\text{take the square root}\\\\\boxed{V=\sqrt{(mv^2)/(M)}}\qquad\text{simplify a bit}

This matches the first choice.

__

Additional comment

Continued simplification would give you ...


V=v\sqrt{(m)/(M)}

However, this is not one of the answer choices.

User Floor
by
2.7k points
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