Make $$ v $$ the subject formula $$ E=\frac{1}{2} m v^{2}+m g h $$

Question

UpStudy AI · Accepted Answer

1. Start with the given equation:
   $$
   E=\frac{1}{2} m v^{2}+m g h
   $$

2. Subtract $$ mgh $$ from both sides:
   $$
   E - mgh = \frac{1}{2} m v^2
   $$

3. Multiply both sides by 2 to eliminate the fraction:
   $$
   2(E - mgh) = m v^2
   $$

4. Divide both sides by $$ m $$ to isolate $$ v^2 $$:
   $$
   v^2 = \frac{2(E - mgh)}{m}
   $$

5. Take the square root of both sides to solve for $$ v $$:
   $$
   v = \sqrt{\frac{2(E - mgh)}{m}}
   $$
$$ v = \sqrt{\frac{2(E - mgh)}{m}} $$

Make the subject formula