You notice you are running low on gas in your 1200kg car, and you are hoping you

Question

You notice you are running low on gas in your 1200kg car, and you are hoping you have enough gas to reach the bottom of the hill. You decide to harness your graitational potential energy combined with your initial kinetic energy at the top of the hill to help you get to the bottom of the hill without over working your engine, so you take your foot off of the gas pedal to coast down the hill. If your initial speed is 10 m/s, the elevation of the hill is 50 m and the work done by friction of the tires on the road is 150,000 J, what will your speed be at the bottom of the hill? Use conservation of energy.

Explanation / Answer

Mass [m] = 1200 kg

Initial Condition :

speed [V1] = 10 m/s

kinetic energy[KE1] = 0.5 *m*v1*v1 = 60000 J

Potential energy [PE1] = m*g*h = 1200*9.8*50 = 588000 J

Final conditions :

speed -> [V2]

kinetic energy[KE2] = 0.5 *m*v2*v2

Potential energy [PE2] = m*g*0 = 0 J

Using Energy conservation :

KE1+PE1-KE2-PE2 = work done by friction

60000 J+ 588000 J- 0.5 *m*v2*v2 = 150000 J

0.5 *m*v1*v2 = 60000 J+ 588000 J- 150000J = 498000 J

V2*V2 = 498000* 2 /1200 = 830

V2 = 28.809 m/s [Ans]

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