If you jump out of an airplane and your parachute fails to open, your downward velocity (in meters per second) t seconds after the jump is approximated by v(t) = 49(1 − (0.8187)^t).

(a) Write an expression for the distance you fall in T seconds.
(b) If you jump from 5000 meters above the ground, estimate, using trial and error, how many seconds you fall before hitting the ground.