# Numerical problem based on parachutist & Terminal Velocity

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

**Question**:

The

force of air resistance Facting on a parachute is given by the equation

F = 83 + 14.6v^{2}

where v is the velocity in m/s and F is measured in newtons (N).

Aparachutistof total weight680 Nis 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 + 14.6v^{2}

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

680 = 83 + 14.6 v^{2}

=> v^{2} = (680-83)/14.6

=> v^{2} = 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.