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For the amusement of the guests, some hotels have elevators on the outside of the building....

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Basic Math

For the amusement of the guests, some hotels have elevators onthe outside of the building. One such hotel is 300 feet high. Youare standing by a window 100 feet above the ground and 150 feetaway from the hotel, and the elevator descends at a constant speedof 30 ft/sec, starting at time

t = 0,

where t is time in seconds. Let θ be the anglebetween the line of your horizon and your line of sight to theelevator.

(a) Find a formula for

h(t),

the elevator's height above the ground as it descends from thetop of the hotel.
h(t) =  

  

(b) Using your answer to part (a), express θ as a functionof time

t.


θ(t) =  

tan−1(2−t5​)



Find the rate of change of θ with respect tot.

dθ
dt

=  



(c) The rate of change of θ is a measure of how fast theelevator appears to you to be moving. At what height is theelevator when it appears to be moving fastest?
h =  

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