### Video Transcript

A skydiver with a mass of 80.0
kilograms falls through air that has a uniform density of 1.23 kilograms per cubic
meter. The skydiver has a surface area of
0.140 meters squared and a drag coefficient of 0.690. What is the skydiver’s terminal
velocity?

We can call this terminal velocity
𝑣 sub 𝑇. And we’ll also write down the
skydiver’s mass, cross-sectional area, drag coefficient, and the density of the air
the skydiver falls through. As the skydiver falls down to
Earth, there’s a gravitational force pulling the skydiver in that direction. Along with the gravitational force,
there’s the drag force resisting the skydiver’s fall. If we recall that drag force is
proportional to the square of an object’s speed, at the start of their fall, the
skydiver has very little drag force. But as they fall faster and faster,
this force increases. And eventually, we get to a point
where the drag force is equal to the gravitational force on the skydiver. At this point, they are no longer
speeding up. They’ve reached terminal
velocity.

We can rewrite 𝐹 sub 𝐷 in terms
of the parameters it relies on. And 𝐹 sub 𝑔, we know, is equal to
the mass of the skydiver times 𝑔, where 𝑔, the acceleration due to gravity, is 9.8
meters per second squared. So one-half the skydiver’s area
times the air density times the drag coefficient times the terminal velocity squared
is equal to the skydiver’s mass times 𝑔. Or 𝑣 sub 𝑇, the skydiver’s
terminal velocity, is the square root of two 𝑚𝑔 divided by 𝐴, the skydiver’s
area, times the density, 𝜚, multiplied by the drag coefficient. When we plug in for all these
values and solve for 𝑣 sub 𝑇, we find it’s equal to 115 meters per second. That’s the maximum speed that this
skydiver will achieve.