Seattle’s Space Needle officially opened on the first day of the Seattle World’s Fair, April 21, 1962. It features a flying saucer-like revolving restaurant 500 feet above the ground. The restaurant is accessible by stairs (832 steps), but most people take an elevator.

Suppose you are across the street having coffee, watching the elevator ascend and descend. Your window is 100 feet above the ground and 2000 feet away from the Space Needle. The elevator ascends and descends at a constant speed of 14 ft/sec. Let be the angle of elevation of your line of sight to the elevator and h(t) is the height of the elevator above ground.

a. Make a prediction. How does d0/dt change? Explain your answer.

b. Write an equation for d0/dt. Explain how that works.

c. Interpret the equation for d0/dt in the context of this problem. What does d0/dt represent physically?

d. at what hight will the elevator be when it appears to be moving fastest? What is 0 at that hight? Use the equation to solve and explain step by step.

e. compare and contrast d0/dt and dy/dt

f. Liga is standing 100 ft away from the space neetle. If Y is the vertical distance from the ground to the laser’s red dot, at what rate is y changing with respect to angle
0 when 0=1 radian?

g. At what rate does y change with respect to angle 0 when liga's laser hits the top of the space needle 605ft?

h. Liga shines her laser at the elevator, which moves at 14 ft/sec. At what rate does 0 change (with respect to time) when the elevator reaches the restaurant, 500 feet above ground? Remember the units!