1. Colossus is approximately 50 meters in diameter and rises 53 meters off the ground. The wheel is equally divided by 20 main spokes from the center of the wheel to the outer rim.
a. Find the increment, in degrees, between the spokes of the wheel around the center of the hub.
b. Find the area of the wheel of Colossus.
c. Find the circumference of Colossus.
d. There is approximately 6195 ft of train track that run throughout the park. If Colossus could fit on the train tracks, approximately how many revolutions of Colossus would it take to cover the distance.
2. By midmorning the Colossus casts a shadow of 117 ft. over level ground while a nearby sign known to be 6 ft tall casts a 4 ft shadow. Determine the
a. height of the wheel to the nearest ft.
b. distance (line of sight) from the end of the shadow to the top of the Colossus.
3. Using the height of the Colossus determined in the above problem to discover the angle of elevation of the sun. Express the answered in:
a. Degrees:
b. Degrees, minutes, and seconds:
4. A fixed position spot light, angled at 40 degrees, is placed at a right angle to the base of Colossus. How far from Colossus should the spot light be placed to illuminate the top of it? (Use height determined in problem 2)
5. The center of Colossus is supported on both sides by steel support masts. The distance from ground level to the center of the wheel is approximately 92 ft. The base support legs of the masts are approximately 108 ft apart. Use the dimensions above to determine:
a. the approximate length of the support legs:
b. the approximate angles between the support legs:
c. the area of the triangle formed by the support legs:
6. It takes __________ (time it) seconds for the Colossus to make one revolution. How long will it take to go around 10 times?
7. How many times can you go around in 5 minutes?
8. Find the area covered by the ground and leg supports.
9. Find the angles each leg support makes with the ground.
10 How far is the center of the Colossus off the ground?
11. Given the radius in meters and speed of rotation (using a timer), find the time to travel one revolution.
12. Using radius = 25m the time (from the previous problem) it takes to go around once, how many times can you go around in 10 minutes?
