QuestionAugust 14, 2025

1 E=(1)/(2)mv^2 Energy of an object in motion Solve for m 2 V=pi r^2h Volume of a cylinder Solve for h 3 4 P=mgh S=2pi r^2+2pi rh Potential Energy Surface area of a cylinder Solve for h Solve for h

1 E=(1)/(2)mv^2 Energy of an object in motion Solve for m 2 V=pi r^2h Volume of a cylinder Solve for h 3 4 P=mgh S=2pi r^2+2pi rh Potential Energy Surface area of a cylinder Solve for h Solve for h
1 E=(1)/(2)mv^2 Energy of an object in motion Solve for m 2 V=pi r^2h Volume of a cylinder Solve for h 3 4 P=mgh S=2pi r^2+2pi rh Potential Energy Surface area of a cylinder Solve for h Solve for h

Solution
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Answer

m = \frac{2E}{v^{2}} ### h = \frac{V}{\pi r^{2}} ### h = \frac{P}{mg} ### h = \frac{S - 2\pi r^{2}}{2\pi r} Explanation 1. Solve for m in kinetic energy formula Given E = \frac{1}{2}mv^{2}, rearrange to solve for m: m = \frac{2E}{v^{2}}. 2. Solve for h in cylinder volume formula Given V = \pi r^{2}h, rearrange to solve for h: h = \frac{V}{\pi r^{2}}. 3. Solve for h in potential energy formula Given P = mgh, rearrange to solve for h: h = \frac{P}{mg}. 4. Solve for h in cylinder surface area formula Given S = 2\pi r^{2} + 2\pi rh, rearrange to solve for h: h = \frac{S - 2\pi r^{2}}{2\pi r}.

Explanation

1. Solve for $m$ in kinetic energy formula<br /> Given $E = \frac{1}{2}mv^{2}$, rearrange to solve for $m$: $m = \frac{2E}{v^{2}}$.<br /><br />2. Solve for $h$ in cylinder volume formula<br /> Given $V = \pi r^{2}h$, rearrange to solve for $h$: $h = \frac{V}{\pi r^{2}}$.<br /><br />3. Solve for $h$ in potential energy formula<br /> Given $P = mgh$, rearrange to solve for $h$: $h = \frac{P}{mg}$.<br /><br />4. Solve for $h$ in cylinder surface area formula<br /> Given $S = 2\pi r^{2} + 2\pi rh$, rearrange to solve for $h$: $h = \frac{S - 2\pi r^{2}}{2\pi r}$.
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