From height to speed
Here's a small miracle of physics: to know how fast a skateboarder is moving
at the bottom of a ramp, you don't need a stopwatch, a camera, or the shape
of the ramp. You only need the height.
The reasoning is energy conservation. At the top, the skater has potential
energy m*g*h and no speed. At the bottom, all of it has become kinetic
energy 0.5*m*v^2 (lesson 5's formula). Set them equal:
m*g*h = 0.5 * m * v^2
The mass appears on both sides - so it cancels. A heavy skater and a light
one hit the bottom at the same speed. Solving for v:
v = sqrt(2 * g * h)
Notice what dropped out: the mass, the ramp's shape, the time it took. Energy
bookkeeping skips all of it and goes straight from height to speed. (Real
ramps lose a little to friction, so this is the ideal ceiling - the real
speed comes out slightly lower.)
The starter shows the shape for a 5 m drop. This lesson's ramp is taller.
Your task: a skater starts from rest at the top of a 12 m ramp. How fast
are they moving at the bottom, in m/s? (g = 9.8)
You'll practice:
- Using energy conservation instead of motion equations
- Reading a derivation where a variable cancels out of both sides