Conservative forces and Mechanical Energy

AI Thread Summary
A 750-kg automobile moving at 20.0 m/s and at a height of 5.0 m coasts down a hill after running out of gas. The conservation of mechanical energy principle is applied, stating that the initial kinetic and potential energy equals the final kinetic and potential energy. The calculations show that the highest position the car reaches above the bottom of the hill is approximately 25.41 m. The final answer, rounded to significant figures, is 25 m. The approach and calculations are confirmed to be correct, with a suggestion to consider significant figures in the final result.
bjudia
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1. A 750-kg 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?a



2. E1=E2 or K1 + U1 = K2 + U2



3. 1/2mv2+mgy=1/2mv2+mgy

1/2(750kg)(20m/s)2+(750kg)(9.8m/s2)(5m)=1/2(750kg)(0m/s)2+(750kg)(9.8m/s2)(Y)

I got y=25.41m or 25m with correct sig figs is that correct?
 
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looks good to me. nice work. You could put in another sig fig in your answer, but I guess it can't be bad to over-estimate the error.
 

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