PreCalculus- Trigonometric Functions Name ______________________________ You have just landed a job for Calcu-Now’s Amusement Park as their newest Civil Engineer. With your stellar math skills and problem solving ability they put you on the job right away. Perhaps not the most thrilling ride, but possibly the most important, you are assigned to the improvement of the Ferris wheel. The Ferris wheel is old and has not been serviced for many years. The park manager acknowledges that people will not be interested in the ride unless some improvements are made. You immediately decide increasing the speed and adding some features will do the trick. Size and Speed You fire up the old Ferris wheel and time a cart making the revolution around the wheel. It takes a minute and 45 seconds for the cart to reach its starting position just like the control panel predicts. The technicians helping you on the job mention that it was built to match the size of the original Ferris Wheel in Chicago. This should give you the information you need to find its current speed. Regulations The IAAPA (Amusement Ride Safety Regulations and Standards Organization) states that Ferris wheel riders should not reach a speed of more than 12 mph or there is a danger that they will be thrown from the cart. The control panel makes the speed an easy adjustment. Its current setting of 1:45 just needs reset. Tracking Position The park manager insists that a system is put in place to track the height of each cart at any moment. You assure the manager that this will be a breeze since the cart oscillates up and down for four oscillations. Camera Feature You also decide to mount a camera 20 feet off the ground to capture the joy of the riders. You will have a camera on both sides of the wheel to catch the riders 20 feet on the way up and 20 feet on the way down. After the Ferris Wheel speed has been increased, you need to time the cameras to fire when the cart reaches 20 feet on both sides. Water Ride As a final thrill feature, you decide to spray the riders with water. One technicians suggests that you time this 15 seconds into the ride. Sounds like a good idea but you are worried it will conflict with the camera shot. You don’t want water getting on the camera. This could make or break your career as a civil engineer. Or worse, cause serious harm to a rider f you don’t design this ride correctly. A lot rests in your hands. Use the information to develop a report that the technicians can use to improve the ride. Include the adjustments needed and use mathematical reasoning to defend your proposal. The cart’s current speed is ____________________________________ mph. Mathematical proof The cart speed should be increased to make a revolution in _____________________ . Mathematical proof  Reset the control panel The height of a cart starting from the ground at time 𝑡 is model by ____________________________ . Mathematical proof graph 1 complete ride The camera should be programmed to take a picture after __________________________________ sec. Mathematical proof Can the water ride be activated after 15 seconds? Why or why not? Mathematical proof After you have done the calculations, summarize your engineering proposal here. What action needs to be taken to make the Ferris wheel thrilling and safe.
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