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:
<u>Speed at the bottom = square root of(2 x gravity x height of the hill)</u>
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 <em>square root </em>of the height, so in order to double your speed, you need to find a hill that's <em>4 times</em> as high.
Atoms are the components of ordinary matter, also called baryonic matter, which only represents 4% of the universe, while the remaining 96% would be formed by what is known as dark matter and dark energy which constitute two of the unsolved problems in physics.
