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. Time to reach 1000 ft under free fall conditions: 1000 = -16t² + 1700 -> 16t² = 700 -> t² = 43.75 -> t = 6.61 sec (t must be positive).

b. Time to reach 930 ft. Same calculations as above with h = 930. Answer is 6.94 sec.

c. The jumper better open the parachute pretty soon or he/she is going to hit the ground (h = 0) after 10.31 secs!!