>>>On your daily drive to work, there's a small hill. You have to drive up one side, then down the other.
>>>
>>>Because you're cheap green, you don't want to use any more fuel than necessary in getting over the hill. After running a few tests, you've discovered that if you approach the bottom of the hill at exactly 50 km/h, you can knock your vehicle out of gear, switch off the engine, and coast to the top. That gives you just barely enough speed to start coasting down the other side, when you can switch your engine back on and put it back in gear.
>>>
>>>One day, though, you're not paying close attention to your speed. When you shift into neutral and switch off your motor at the bottom of the hill, you notice you're going 60 km/h instead of 50 km/h.
>>>
>>>How fast will you be going at the top of the hill?
>>>
>>>(techie types: ignore differences in aerodynamic drag and rolling resistance)
>>
>>Going up the hill, decelerates from 50 km/h to 0 km/h
>>If you start at 60 km/h I'd say that your speed at the top of the hill will be 10 km/h - well a bit above 10 km/h since you had a little speed left when starting at 50 km/h
>
>That would be the "intuitive" answer.
>
>Using conservation of energy, according to my calculations it would be about 33 km/h.
>
>I have a test hill here - if I hit the bottom at 76 km/h I roll to a perfect stop at the top. If I'm only a few km/h "hot" at the bottom, I'm doing 15 - 20 km/h at the top.

How many times have you tested this.

Are you known as "Al stops on the hill" locally