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- jackiepc1128 15.00

## Answers

## BettieZumbrunnen

Your potential energy at the top of the hill was (mass) x (gravity) x (height) .

Your kinetic energy at the bottom of the hill is (1/2) x (mass) x (speed)² .

If there was no loss of energy on the way down, then your kinetic energy

at the bottom will be equal to your potential energy at the top.

(1/2) x (mass) x (speed)² = (mass) x (gravity) x (height)

Divide each side by 'mass' :

(1/2) x (speed)² = (gravity) x (height) . . . The answer we get

will be the same for every skater, fat or skinny, heavy or light.

The skater's mass doesn't appear in the equation any more.

Multiply each side by 2 :

(speed)² = 2 x (gravity) x (height)

Take the square root of each side:

Speed at the bottom = square root of(2 x gravity x height of the hill)

We could go one step further, since we know the acceleration of gravity on Earth:

Speed at the bottom = 4.43 x square root of (height of the hill)

This is interesting, because it says that a hill twice as high won't give you

twice the speed at the bottom. The final speed is only proportional to the

square root of the height, so in order to double your speed, you need to

find a hill that's 4 times as high.