Let denote the speed at time seconds after jumping from a large height of a man falling with a parachute for which the combined weight of man plus parachute is 192 pounds. The man opens the parachute after 10 seconds. Before the chute is open air resistance is given by pounds. While the parachute is open air resistance is given by pounds. Assuming acceleration due to gravity is 32 feet per second squared, find explicit formulas for . (Use the approximation .)

We are given that the weight of the man plus parachute is and that . Therefore . So, for we have and

If , then we have and , therefore,

So, we apply Theorem 8.3 (page 310 of Apostol) with

Therefore,