Question

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

Answer 1

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.