Question help a smoke jumper jumps from a plane that is 19001900 ft above the ground. the function h equals negative 16 t squared plus 1900h=−16t2+1900 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 940940 ft?
c. what is a reasonable domain and range for the function h?

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barnuts barnuts · Answer 1 · 2017-11-27T13:02:31+01:00

A. Starting at 1900 ft, so if he opened his parachute at 1000 ft, therefore this means that h = 1000:

h = - 16t^2 + 1900

1000 = - 16 t^2 + 1900

t = 7.5 seconds

B. So we have h = 940

940 = - 16 t^2 + 1900

t = 7.746 seconds

C. The domain will always be time and since time starts at zero, so it is the initial point for h:

h = - 16(0)^2 + 1900

h = 1900

We also know that at lowest point h = 0, so the last value of t is:

0 = - 16 t^2 + 1900

t = 10.897 seconds

Therefore

domain: (0, 10.897)

range: (1900, 0)