John has been hired to design an exciting carnival ride. Tiff, the carnival owne

Question

John has been hired to design an exciting carnival ride. Tiff, the carnival 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: (i) the wheel should rotate counterclockwise with an angular speed of a = 15 RPM; (ii) the linear speed of a rider should be 200 mph; (iii) the lowest point on the ride should be c = 4 feet above the level ground. Find the radius of the ferris wheel. (Round your answer to two decimal places.) Once the wheel is built, John suggests that Tiff should take the first ride. The wheel starts turning when Tiff is at the location P, which makes an angle theta with the horizontal, as pictured. It takes her 1.3 seconds to reach the top of the ride. Find the angle theta. (Round your answer to two decimal places.) theta = rad Poor engineering causes Tiff's seat to fly off in 6 seconds. Describe where Tiff is located (an angle description) the instant she becomes a human missile. (Give your answer as an angle measured counterclockwise from her starting point P.) rad

Explanation / Answer

For part 1 we will answer like that way .

15 rpm ·( 2r ft/ 1 revolution)· (1 mile / 5280 ft) · (60 minutes / 1 hour) = 200 miles / hour it is the method of conversion revolution per minute into hours.

Now w e have to find the radius , for this we will

(15r)/44 miles / hour = 200 miles/hour

(15r)/44 = 200

15r = 8800

r = 8800 / (15)

r = 186.84 ft. answer

Part b -> we have period = 60/15

so in 1.3 seconds we will have

=1.3/(60/15) =0.325

so we will have finally 0.325-0.25=0.075 radians answer

for part c -> The top of the wheel takes 1.3 seconds, then from the top of the wheel until Tiff becomes a human missile is (6-1.3=4.7 seconds) seconds

so we will have 4.7/(60/15) =4.7/4=1.175 radians answer

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