Numerical problem based on parachutist & Terminal Velocity

Last updated on February 8th, 2024 at 10:06 am

Question:

The force of air resistance F acting on a parachute is given by the equation
F = 83 + 14.6v²
where v is the velocity in m/s and F is measured in newtons (N).
A parachutist of total weight 680 N is descending,
Calculate the terminal velocity of the parachutist.

Solution:

At terminal velocity, air resistance equals their weight.

Weight of the parachutist = 680 kg
Air resistance formula for this case: F = 83 + 14.6v²

When, air resistance F = 680 kg, then the velocity v becomes the terminal velocity.

680 = 83 + 14.6 v²
=> v² = (680-83)/14.6
=> v² = 40.9
v = 6.39 m/s (terminal velocity)

Try yourself/assignment

Use the equation given above to explain why a heavier parachutist reaches a higher terminal velocity.