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A bicyclist climbs a hill 17 m tall and then coasts down the other side without pedaling. If the...

Question:

A bicyclist climbs a hill 17 m tall and then coasts down the other side without pedaling. If the cyclist's speed was 2.5 m/s at the top, what is it at the bottom (ignoring friction)?

Conservation Of Energy:

From the law of conservation of energy, Energy stored within the system must remain constant for example mechanical energy which consists of sum of potential energy, as well as kinetic energy, must remain constant during the conversion.

Answer and Explanation:

Given

The height of the hill is {eq}h=17\ m {/eq}

The initial speed of the bicyclist at the top of the hill is {eq}u=2.5\ m/s {/eq}

Now from the conservation of energy:

{eq}mgh=\frac{1}{2}m(v^2-u^2)\\ (9,81\times 17)=\frac{1}{2}(v^2-2.5^2)\\ 333.54=v^2-6.25\\ v^2=339.79\\ v=18.43\ m/s {/eq}

Thus, the speed of cyclist at the bottom is 18.43 m/s


Learn more about this topic:

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Energy Conservation and Energy Efficiency: Examples and Differences

from Geography 101: Human & Cultural Geography

Chapter 13 / Lesson 9
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