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A smoke jumper jumps from a plane that is 18001800 ft above the ground. the function h equals negative 16 t squared plus 1800h=â16t2+1800 gives theâ 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 1000â ft?
b. how long is the jumper in free fall if the parachute opens at 950950 âft?
c. what is a reasonable domain and range for the functionâ h?
a. the jumper is in free fall for nothing s if the parachute opens at 1000 ft. â(round to two decimal places asâ needed.)

Respuesta :

The initial height above ground is 1800 ft.

The height (ft) above ground at time t seconds is
h(t) = 1800 - 16t²

Part a.
If the parachute opens when h = 1000 ft, then
1000 = 1800 - 16t² 
16t² = 18000 - 1000 = 17000
t² = 17000/16

Answer: t = 32.60 s

Part b.
If the parachute opens when h = 950 ft, then
16t² = 18000 -950 = 17050
t² = 17050/16

Answer: t = 32.64 s

Part c.
It is not reasonable for the parachute to open at less than 500 ft from the ground, else the parachutist may suffer landing harm.

If h = 500, then
16t² = 18000 - 500 = 17500
t = 33.07 s
If h = 18000, then
t² = 18000/16
t = 33.54 s

Answer:
A reasonable domain for h is t =(33.07, 33.54) s.
A reasonable range for h is (500, 18000) ft.

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