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.
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?
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).