Question

A skydiver with a mass of 54.9 kg achieves a terminal speed of 53.4 m/s without deploying her parachute. We assume that the drag force acting on her is proportional to the square of her speed, expressed as F_drag = kv². What is the constant of proportionality, k? (Assuming the gravitational acceleration is 9.8 m/s².)

Answer 1

The constant of proportionality, k, for the drag force acting on a skydiver at terminal velocity can be calculated by setting the drag force equal to the skydiver's weight. For a skydiver with a mass of 54.9 kg and a terminal speed of 53.4 m/s, the value of k is approximately 0.202 kg/m.

Step-by-step explanation:

To find the constant of proportionality, k, for the drag force acting on a skydiver reaching terminal velocity, we can set the formula for drag force Fdrag = kv² equal to the weight of the skydiver, which is the product of mass (m) and gravitational acceleration (g).

At terminal speed, Fdrag equals the gravitational force, so:

• mg = kv²

Using the given values of m = 54.9 kg, g = 9.8 m/s², and terminal velocity v = 53.4 m/s, the equation becomes:

• (54.9 kg)(9.8 m/s²) = k(53.4 m/s)²

Solving for k gives:

• k = (54.9 kg)(9.8 m/s²) / (53.4 m/s)²
• k ≈ 0.202 kg/m

The constant of proportionality, k, for the skydiver is approximately 0.202 kg/m.