# Just as a car tops a 47-meter high hill with a speed of 36 km/h, it runs out of gas and coasts...

## Question:

Just as a car tops a 47-meter high hill with a speed of 36 km/h, it runs out of gas and coasts from there, without friction or drag. How high, to the nearest meter, will the car coast up the next hill?

## Kinetic energy:

The term kinetic energy is considered only when the body possesses motion. The kinetic energy directly varies the velocity of the object. In S.I system, its measurable unit is Joules.

## Answer and Explanation:

Given data:

• The initial height of the car is {eq}{h_1} = 47\,{\rm{m}} {/eq}
• The speed of the car on the hill is {eq}v = 36\,{\rm{km/h}} = \left( {\dfrac{{36 \times 1000}}{{3600}}} \right)\,{\rm{m/s}} {/eq}

As from the given data, to climb the next hill there will be only the potential energy exists.

The expression for the conservation of energy is

{eq}\begin{align*} mg{h_2} &= mg{h_1} + \dfrac{1}{2}m{v^2}\\ {h_2} &= {h_1} + \dfrac{1}{{2g}}{v^2} \end{align*} {/eq}

Substituting the values in the above equation as,

{eq}\begin{align*} {h_2} &= {h_1} + \dfrac{1}{{2g}}{v^2}\\ {h_2} &= 47 + \dfrac{1}{{2 \times 9.8}}\left( {\dfrac{{36 \times 1000}}{{3600}}} \right)\\ {h_2} &= 47 + 0.510\\ {h_2} &= 47.510\,{\rm{m}} \end{align*} {/eq}

Thus the height of the next hill is {eq}{h_2} = 47.510\,{\rm{m}} {/eq}

#### Learn more about this topic:

Energy Conservation and Energy Efficiency: Examples and Differences

from Geography 101: Human & Cultural Geography

Chapter 13 / Lesson 9
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