Question

Problem 17.1 John has been hired to de- sign an exciting carnival ride. Tiff, the car- nival owner, has decided to create the world's greatest ferris wheel. Tiff isn't into math; she simply has a vision and has told John these constraints on her dream: () the wheel should rotate counterclockwise with an angular speed of 12 RPM: (i) the linear speed of a rider should be 200 mph) the lowest point on the ride should be 4 feet above the level ground. Recall, we worked on this in Exercise 16.5. 12 RPM 4 feet (a) Impose a coordinate system and find the coordinates T(t) (x(t),y(t)) of Tiff at time t seconds after she starts the ride. (b) Tiff becomes a human missile after 6 seconds on the ride. Find Tiff's coordi- nates the instant she becomes a human missile. (c) Find the equation of the tangential line along which Tiff travels the instant she becomes a human missile. Sketch a pic- ture indicating this line and her initial direction of motion along it when the seat detaches

Answer 1

uI 12 P pm Theheelis sototing a 1 3pm which is 00 m Since e whee is in Lisculor metion, hence ) ě - 160 miles sumng esigin is al the centve of the wheel so the position of anypinton the drcle will be gin1S o Centoe (0) (ces ot, sin cot)

3T t stn 5 t o, titf a the point P(xo, yo)so, Since at is In 1 tiff eaches the point , 3ao.000 51516 100 3o at t-6s the pesiton o f will be, q abeve 8 the angle is 9 50 50