Epic calculus question. only a true genius can tackle it.?

For the amusement of the guests, some hotels have elevators on the outside of the building. One such hotel is 200 feet high. You are standing by a window 100 feet above the ground and 150 feet away from the hotel, and the elevator descends at a constant speed of 30 ft/sec, starting at time t = 0, where t is time in seconds. Let 胃 be the angle between the line of your horizon and your line of sight to the elevator.http://www.webassign.net/userimages/66603?db=v4net


(a) Find a formula for h(t), the elevator's height above the ground as it descends from the top of the hotel.


(b) Using your answer to part (a), express 胃 as a function of time t. Remember to use atan for arctan.


Find the rate of change of 胃 with respect to t.


(c) The rate of change of 胃 is a measure of how fast the elevator appears to you to be moving. At what time does the elevator appear to be moving fastest?


At what height does the elevator appear to be moving fastest?Epic calculus question. only a true genius can tackle it.?
Okay





(a) h(t) = 200 - 30 t





(b) tan 胃 = (200 - 30 t) / 150 = 4/3 - 1/5 t


=====%26gt; 胃 = atan ( 4/3 - 1/5 t )





d胃/dt = 1 / [ (4/3 - 1/5 t)^2 + 1 ] * (-1/5)





now maximize d胃/dt





d胃/dt = -1 / [ 5 ((4/3 - t/5)^2 + 1) ]





d(d胃/dt) / dt = [5 (4/3-t/5)^2 + 1]^(-2) * (2 (4/3 - t/5) (-1/5)





set = 0 4/3 - t/5 = 0


t/5 = 4/3


t = 20/3


time fastest is 20/3


the height is h(20/3) = 200 - 30(20/3) = 200 - 200 = 0





AT THE END?? height is zero????


mmmm?