[couga]

The engine of a 1950 kg car driving at 25m/s suddenly dies out as it approaches a 25 m high hill. Will the car have enough energy to clear this hill?

[Capuchin]

Work out the kinetic and the potential energy needed, compare and there's your answer.

[catgita]

With no air or mechanical drag the mass and energy of the car is irrelevant. If you were to drop the car from 25m, would it be going 25m/s when it hit the ground?

I can't recall the math at the moment, other than acceleration due to gravity is 9.8m/s/s. A napkin calculation says it comes up a little short. I think you could clear a 30m hill at 30m/s, but at 25m/s you only make about 22m up, 20m/s you make 15m, etc.

[Capuchin]

You're making it too complex catgita.

At the bottom of the hill, the car has KE = = 0.5*1950*25*25 J
At the top of the hill, the car must have PE = = 1950*25*9.8 J

As the KE is > the PE, the car makes it over the hill. As it has enough KE to convert into PE.

I don't understand your method of doing the sum. I don't see how you are able to do it that way without knowing more information.

[catgita]

For one, the mass cancels out when you have:
1/2mv^2>mgh
giving you
1/2v^2>gh

Second, maybe you have heard of someone called Newton? Drop a hammer, drop a feather from 25m, which hits the ground first? Make the car 1kg or 1,000,000kg, no difference.

Regardless, you are correct, the car makes it to the top going about 11.6m/s. Thanks for the equasions, much better than my estimates.;)

[Capuchin]

Of course you're right, but you're just confusing things for our high school friend here. :)