Solve mgh=1/2mv^2+1/2(2/5)mr^2(v^2/r^2) for v

[math_celebrity]

Solve mgh=1/2mv^2+1/2(2/5)mr^2(v^2/r^2) for v

1/2(2/5) = 1/5 since the 2's cancel
r^2/r^2 = 1

So we simplify, and get:
mgh=1/2mv^2+1/5(mv^2) for v

Divide each side by m, so m's cancel in each term on the left and right side:
gh = 1/2v^2 + 1/5(v^2)

Combine like terms for v^2 on the right side:
1/2 + 1/5 = 7/10 from our fraction calculator

So we have:
gh = 7v^2/10

Multiply each side by 10:
10gh = 7v^2

Now divide each side by 7
10gh/7 = v^2

Take the square root of each side:
v = sqrt(10gh/7)