Chapter 6.3, Problem 7E

Reminder Round all answers to two decimal places unless otherwise indicated.

Falling with a parachute When an average-sized man with a parachute jumps from an airplane, he will fall $S=12.5\left({0.2}^t-1\right)+20t$ feet in $t$ seconds.

a. Plot the graph of $S$ versus $t$ over at least the first $10\text{seconds}$ of the fall.

b. How far does the parachutist fall in $2\text{ seconds}$?

c. Calculate $\frac{dS}{dt}$ at $2\text{ seconds}$ into the fall and explain what the number you calculated means in practical terms.