Challenge Problems (Problem 133)

A skydiver is at an altitude of 1520 m. After 10.0 seconds of free fall, he opens his parachute and finds that the air resistance, $F_{\text{D}}$, is given by the formula $F_{\text{D}}=\text{−}bv,$ where b is a constant and v is the velocity. If $b=7.50,$ and the mass of the skydiver is 82.0 kg, first set up differential equations for the velocity and the position, and then find: (a) the speed of the skydiver when the parachute opens, (b) the distance fallen before the parachute opens, (c) the terminal velocity after the parachute opens (find the limiting velocity), and (d) the time the skydiver is in the air after the parachute opens. Select the answer to part (a).