A smoke jumper jumps from a plane that is 1800 ft above the ground. The function h=-16t^2+1800 gives the​ jumper's height h in feet during the free fall at t seconds.

Question

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

Answer 1

To find the time the parachute opens at a certain height, we need to solve the equation h = -16t^2 + 1800 for t. Let's solve this equation for each given height:

a. For h = 1000 ft:
1000 = -16t^2 + 1800
Rearranging the equation:
-800 = -16t^2
Dividing both sides by -16:
50 = t^2
Taking the square root of both sides:
t = ±√50

Since we are talking about time, the negative value doesn't make sense in this context.
So, the jumper is in free fall for √50 seconds.

b. For h = 940 ft:
940 = -16t^2 + 1800
Rearranging the equation:
-860 = -16t^2
Dividing both sides by -16:
53.75 = t^2
Taking the square root of both sides:
t ≈ ±√53.75

Again, the negative value doesn't make sense in this context.
So, the jumper is in free fall for approximately √53.75 seconds.

c. The reasonable domain for the function h = -16t^2 + 1800 is t ≥ 0, since time cannot be negative.
The reasonable range for the function h is 0 ≤ h ≤ 1800, since the height cannot go below 0 (ground level) or exceed 1800 ft (initial height above the ground).