Given the equation mgh = (1/2)mv^2, what is the expression for height (h) in terms of velocity (v) and gravitational acceleration (g)?

• A. h = v^2 / (2g)
• B. h = g / (2v^2)
• C. h = v^2 / g
• D. h = 2v^2 / g

Answer: (A)

Verified step by step guidance

1. Start with the given equation for mechanical energy conservation: $mgh=\frac{1}{2}m{v}^2$.
2. Notice that the mass $m$ appears on both sides of the equation. You can divide both sides by $m$ to simplify: $gh=\frac{1}{2}{v}^2$.
3. To isolate $h$, divide both sides of the equation by $g$: $h=\frac{\frac{1}{2}}{v^2}$.
4. Simplify the expression by rearranging the terms: $h=\frac{v^2}{2g}$.
5. The expression for height $h$ in terms of velocity $v$ and gravitational acceleration $g$ is $h=\frac{v^2}{2g}$.