Final answer:
a. The jumper is in free fall for 7.5 seconds when the parachute opens at 1000 ft. b. The jumper is in free fall for 7.7 seconds when the parachute opens at 950 ft. c. A reasonable domain for the height function is 0 to the time it takes for the parachute to open and the range is the height of the parachute opening to 1900 ft.
Step-by-step explanation:
a. To determine the time the jumper is in free fall when the parachute opens at 1000 ft, we can set the height function h equal to 1000 and solve for t.
-16t²+1900=1000
-16t²=-900
t²=56.25
t=7.5
Therefore, the jumper is in free fall for 7.5 seconds when the parachute opens at 1000 ft.
b. Following the same process, we can set h equal to 950 and solve for t.
-16t²+1900=950
-16t²=-950
t²=59.375
t=7.7
The jumper is in free fall for 7.7 seconds when the parachute opens at 950 ft.
c. The height function h represents the jumper's height during free fall. Since the jumper starts at a height of 1900 ft and the maximum height is determined by the time it takes for the parachute to open, a reasonable domain for the function h is 0 to the time it takes for the parachute to open. The range of the function h is the height of the parachute opening to 1900 ft.