A smoke jumper jumps from a plane that is 1700 ft above the ground. The function h=−16t2+1700 gives the jumper's height h in feet during the free fall at t seconds.

Question

A smoke jumper jumps from a plane that is 1700 ft above the ground. The function h=−16t2+1700 gives the jumper's height h in feet during the free fall at t seconds.

a. How long is the jumper in free fall if the parachute opens at 1000​ ft?

b. How long is the jumper in free fall if the parachute opens at 930 ​ft?

c. What is a reasonable domain and range for the function​ h?

Answer 1

h = −16t² + 1700

a) 1000 = −16t² + 1700

700 = 16t²

Solve for t using square roots. Use the positive root since we can't go back in time.

b) 930 = −16t² + 1700

770 = 16t²

Solve for t using square roots. Again, use the positive root.

c) The range (height) will be 0 to 1700 feet. The smoke jumper starts at 1700 feet and lands at 0 feet. He can't get higher or lower. The domain (time) will be 0 to the time it takes for the jumper to reach the ground. Set h =0 and solve for t like you did in a) and b).