Falling with a parachute: if an average-size man jumps from an airplane with an open parachute, his downward velocity t seconds into the fall is v(t) = 20(1 - 0.2^t) feet per second.
a. use functional notation to express the velocity 2 seconds into the fall, and then calculate it.
b. explain how the velocity increases with time. include in your explanation the average rate of change from the beginning of the fall to the end of the first second and the average rate of change from the fifth second to the sixth second of the fall.
c. find the terminal velocity.
d. compare the time it takes to reach 99% of terminal velocity here with the 25 seconds it took a skydiver with his parachute closed to reach 99% of terminal velocity in example 2.1. on the basis of the information we have, which would you expect to reach 99% of terminal velocity first, a feather or a cannonball?