Inverse Relations and Functions Precalculus

Question

FIRE FIGHTING Airplanes are often used to drop water on forest fires in an effort to stop the spread of the fire. The time in seconds it takes for the water to travel from the plane to the ground is given by the function t(h)=sqrt(h)/4, where h is given in feet. Find the inverse of the function. If the water takes 6 seconds to hit the ground, from what height did the plane drop the water?

Answer 1

FIRE FIGHTING Airplanes are often used to drop water on forest fires in an effort to stop the spread of the fire. The time in seconds it takes for the water to travel from the plane to the ground is given by the function t(h)=sqrt(h)/4, where h is given in feet. Find the inverse of the function. If the water takes 6 seconds to hit the ground, from what height did the plane drop the water?

y =√h/4

For Inverse

x= √y/4

x² = y/16

so Y= 16x²

Inverse function is

t^-1 (h) = 16 h²

For 6 seconds h = 0

using h = 16 t²

for 6 sec

h = 16*36

= 576 ft