a. To find the time when the jumper's height is 1000 ft, we can substitute h = 1000 into the equation h = -16t^2 + 1800 and solve for t.
-16t^2 + 1800 = 1000
-16t^2 = -800
t^2 = 800/16
t^2 = 50
t = sqrt(50) or t ≈ 7.07 seconds
Therefore, the jumper is in free fall for approximately 7.07 seconds when the parachute opens at 1000 ft.
b. Similarly, to find the time when the jumper's height is 950 ft, we substitute h = 950 into the equation h = -16t^2 + 1800 and solve for t.
-16t^2 + 1800 = 950
-16t^2 = -850
t^2 = 850/16
t^2 ≈ 53.125
t ≈ sqrt(53.125) or t ≈ 7.29 seconds
Therefore, the jumper is in free fall for approximately 7.29 seconds when the parachute opens at 950 ft.
For the reasonable range of the function h, we need to consider the physical context. The jumper starts from a height of 1800 ft and falls towards the ground, so the height should be positive and cannot exceed the initial height. Therefore, a reasonable range for the function h is 0 < h < 1800.
For the reasonable domain of the function h, we can look at the time of free fall. The jumper is in free fall for a certain amount of time, and we are given that the parachute opens at a certain height. Therefore, the reasonable domain for the function h is 0 < t < some positive value (in this case, the time when the parachute opens).