Table of contents

9. Work & Energy

Intro to Energy & Kinetic Energy

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Multiple Choice

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

h = v^2 / (2g)

h = g / (2v^2)

h = v^2 / g

h = 2v^2 / g

Verified step by step guidance

Start with the given equation for mechanical energy conservation:

m g h = \frac{1}{2} m v^{2}

Notice that the mass

m

appears on both sides of the equation. You can divide both sides by

m

to simplify:

g h = \frac{1}{2} v^{2}

To isolate

h

, divide both sides of the equation by

g

h = \frac{\frac{1}{2}}{v^{2}}

Simplify the expression by rearranging the terms:

h = \frac{v^{2}}{2 g}

The expression for height

h

in terms of velocity

v

and gravitational acceleration

g

h = \frac{v^{2}}{2 g}

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