Question

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?

Answer 1

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)