A biologist standing at the bottom of an 80-foot vertical cliff watches a peregrine falcon dive from the top of the cliff at a 45° angle from the horizontal (see figure). 

a. Express the angle of elevation θ from the biologist to the falcon as a function of the height h of the bird above the ground. The vertical distance between the top of the cliff and the falcon is 80 - h.)

b. What is the rate of change of θ with respect to the bird's height when it is 60 feet above the ground?

Transcribed Image Text:

45° Falcon 80 ft Flight path Biologist