A sky diver of mass 80.9 kg (including outfit and equipment) floats down suspended from her parachute, having reached terminal speed. The drag coefficient is 0.575, and the area of her parachute is 20.27 m2. The density of air is 1.14 kg/m3. What is the air's drag force on her? (upward is positive, downward negative)
To calculate the drag force experienced by the skydiver, we can use the drag force equation:
Drag force = (1/2) * drag coefficient * density of air * velocity^2 * area.
In this case, the velocity of the skydiver is constant, as she has reached terminal speed. Therefore, her velocity can be denoted as "v."
Let's plug in the given values into the equation:
Drag force = (1/2) * 0.575 * 1.14 kg/m^3 * v^2 * 20.27 m^2.
Next, we'll need to rearrange the equation to solve for the drag force (Fd):
Fd = (1/2) * 0.575 * 1.14 kg/m^3 * v^2 * 20.27 m^2.
Now, we just need to multiply the remaining terms:
Fd = 0.2910765 kg/m^3 * v^2 * 20.27 m^2.
Since we're given the mass of the skydiver (80.9 kg) and the density of air (1.14 kg/m^3), we can determine the gravitational force acting on the skydiver:
Gravity force = mass * gravitational acceleration.
Gravity force = 80.9 kg * 9.8 m/s^2.
Now, we can equate the gravitational force to the drag force:
Gravity force = Drag force.
80.9 kg * 9.8 m/s^2 = 0.2910765 kg/m^3 * v^2 * 20.27 m^2.
Now, we can solve for v:
v^2 = (80.9 kg * 9.8 m/s^2) / (0.2910765 kg/m^3 * 20.27 m^2).
v^2 = 268.94 m^2/s^2.
Taking the square root of both sides, we find:
v = 16.4 m/s.
Now that we know the velocity, we can calculate the drag force:
Fd = 0.2910765 kg/m^3 * (16.4 m/s)^2 * 20.27 m^2.
Fd ≈ 187.18 N.
Therefore, the air's drag force on the skydiver (upward is positive, downward is negative) is approximately 187.18 N.