Why Don’t Downhill Skiers Keep on Accelerating?

In the super-G, skiers can reach speeds

of over 100 miles an hour.

But why stop there?

Why don't they keep on speeding up forever?

If you think about the forces on a skier,

you can think of three.

There's gravity pulling down.

There's the snow pushing up this way,

perpendicular to the snow,

and then there's some friction force.

It's pretty small, but it is there.

If you use those equations and forces,

you can calculate the acceleration.

It depends on the angle of the incline,

the coefficient of friction.

But once you have an acceleration,

you're just gonna keep on speeding up forever.

But you don't, because there's another force.

We actually have another force on here,

due to air.

So there's an air resistance force,

and the important thing is that air resistance force

increases with velocity.

One way we can model that is by saying

it's proportional to the velocity squared.

So at one point you're gonna reach a speed

where the downward pulling component of gravity

is equal to friction, plus the air resistance force,

and you would reach terminal velocity.

So you're not gonna keep on speeding up.

The same thing happens when people jump out of an airplane.

As you fall, you increase the speed

until the upward pushing air resistant force

is equal to the downward gravitational force.

No more acceleration.

Terminal velocity.

You don't keep on speeding up.