A 513 kg automobile is moving at 27.0 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?

Question

roadjester · Answer

so we're assuming that the car did NOT stop when it ran out of gasoline?

anonymous · Answer

well the car ran out of gasoline, but it kept moving uphill until it came to a stop

roadjester · Answer

ok then I'm going to say this.
The car has both kinetic and potential energy

roadjester · Answer

$K=\frac 1 2 mv^2$ and $u=mgh$

anonymous · Answer

so does this have to do something with mechanical energy? where the sum of the above forces equals mechanical?

anonymous · Answer

Ki+Ui=Kf+Uf

roadjester · Answer

That's kinda what I'm going for although I'm not as confident on this one. Do yiou by any chance have the correct answer?

anonymous · Answer

i wish, i tried googling it but got nothing

roadjester · Answer

because see, we know what the initial velocity is; that's given, but when it's coasting we don't know the final velocity so we don't know the final kinetic energy. You follow?

anonymous · Answer

wouldn't the final velocity be zero since it came to a stop at the end?

roadjester · Answer

when it runs out of gasoline it still coasts down the hill

roadjester · Answer

this means it still has kinetic energy

roadjester · Answer

@ybarrap Can you help me out here?

anonymous · Answer

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