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Problem:An automobile is moving at 20.0 m/s at a height of 5.0 m above the bottom of a hill when it runs out of gasoline. The car coasts down the hill and then continues coasting up the other side until it comes to rest. Ignoring frictional forces and air resistance, what is the value of h, the highest position the car reaches above the bottom of the hill?

Respuesta :

Answer:25.40 m

Explanation:

Given

velocity of automobile(v)=20 m/s

height =5 m

Let h be the final height car can coast after running out of gasoline and final velocity will be zero

Conserving Energy at two points

[tex]E_1=E_2[/tex]

[tex]E_1=Potential\ Energy + Kinetic\ Energy[/tex]

[tex]E_1=m g h_0+\frac{mv^2}{2}[/tex]

[tex]E_1=m\times 9.8\times 5+\frac{m\times 20^2}{2}[/tex]

[tex]E_2=Potential Energy[/tex]

[tex]E_2=m\times 9.8\times h [/tex]

[tex]9.8\times 5+\frac{400}{2}=9.8\times h[/tex]

[tex]h=\frac{249}{9.8}=25.40 m[/tex]

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