A smoke jumper jumps from a plane that is 1800 ft above the ground. The function h=-16^2 + 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 950 ft?
What is a reasonable range for the function h?
-1800<h<1800
0<h<1800
-10<h<10
0<h<10
All real numbers
What is a reasonable domain for the function h?
0<t<10
0<t<1800
-1800<t<1800
-10<t<10
All real numbers
so, in the 6 hours since you last posted this, have you made any headway in the solution?
(a) solve -16t^2 + 1800 = 1000
(b) solve -16t^2 + 1800 = 950
surely, knowing what you do about parabolas, you can determine the range, since the vertex is at (0,1800) and the parachute does not burrow into the ground.
and the domain is surely only during the actual fall time 0 < t < √(1800/16)
don't get spooked by the equations and stuff -- think about the actual meaning and events happening.
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).
a. To find the time when the parachute opens at 1000 ft, we need to set the height h equal to 1000 ft and solve for t:
-16t^2 + 1800 = 1000
-16t^2 = 1000 - 1800
-16t^2 = -800
Divide both sides by -16:
t^2 = (-800)/(-16)
t^2 = 50
Taking the square root of both sides:
t = ±√50
Since time cannot be negative, t = √50 ≈ 7.07 seconds.
Therefore, the jumper is in free fall for approximately 7.07 seconds if the parachute opens at 1000 ft.
b. To find the time when the parachute opens at 950 ft, we need to set the height h equal to 950 ft and solve for t:
-16t^2 + 1800 = 950
-16t^2 = 950 - 1800
-16t^2 = -850
Divide both sides by -16:
t^2 = (-850)/(-16)
t^2 = 53.125
Taking the square root of both sides:
t = ±√53.125
Since time cannot be negative, t = √53.125 ≈ 7.29 seconds.
Therefore, the jumper is in free fall for approximately 7.29 seconds if the parachute opens at 950 ft.
The reasonable range for the function h is 0 < h < 1800, since height cannot be negative and the maximum height is given as 1800 ft.
The reasonable domain for the function h is all real numbers since time can be any positive value.