Just as a car tops a 54 meter high hill with a speed of 33 km/h it runs out of gas and coasts from there,?

Question

without drag or friction. How high will the car coast up the next hill?

Answer 1

Total energy on top of the hill TE(H) = PE(H) + KE(H) = mgH + 1/2 mv^2; where H = 54 m and v = 33 kph.

Total energy at h height on the next hill TE(h) = PE(h); where there is no more kinetic energy because the car is stopped.

From the conservation of energy the two TE's are equal; so we have TE(H) = mgH + 1/2 mv^2 = mgh = TE(h).

Then solving for h = (gH + v^2/2)/g; where g = 9.81 m/sec^2, H = 54 m, v = 33 kph (don't forget to convert this to mps), and you have everything on the RHS to work the problem.

The physics is this...because of the conservation of energy, the two total energies are the same value because energy is neither created nor destroyed. But the makeup of the TE's differs as energy can be and is converted from one form to another.

Answer 2

Check all the levels of fluids when possible, then again I always get an oil change when the car indicates it to me, so the levels are always correct. I only take my car to places I've read reviews about and know that the service is legit and nothing is forgotten. Although I drive a minivan, I've always used Silver or mid-grade gasoline and while I don't always go to the big brand gas stations I make sure the octane level is to my satisfaction. Otherwise I'll drive further looking for good octane. I don't do this every time, but sometimes I'll allow my car a minute or two to sit just after starting the car. I never run the car too hard and if I travel cross country I'll take a few stops to allow the car to cool. (Not sure if that's necessary) Once every 6 months have the tires rotated and checked. I've got a Honda and I'll tell you over the last 20 years with them I've spent thousands of dollars less money on Honda maintenance then on my Chevy cars.

Answer 3

None. The power steering dies and the driver fails to be able to turn the wheel and runs off the side of the hill.

But the real answer is found by equating the kinetic energy to the potential energy where you will find that the mass cancels out. The highest point you can get to is when the car stops and all the kinetic energy is now potential energy.

So kinetic energy=0.5 * mv^2
Potential energy is = m*g*h

so eliminating m we get h=v^2/(2g)
(don't forget to show your working!)
go plug and chug to find h
and don't forget to add this to the original 54m

The cool thing about this is that it shows that mass makes no difference to the result. It could be a marble or a freight train rolling up and down and you would get to the same height.