a) [in feet] b) [in radians] c) [in radians] ohn has been hired to design an exc

Question

a) [in feet]

b) [in radians]

c) [in radians]

ohn 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-12 RPM; (i) the linear speed of a rider should be 250 mph; (i) the lowest point on the ride should be c-3 feet above the level ground a RPM c feet (a) Find the radius of the ferris wheel. (Round your answer to two decimal places.) ft (b) 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 with the horizontal, as pictured. It takes her 1.3 seconds to reach the top of the ride. Find the angle . (Round your answer to two decimal places.) rad (c) 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.) rvad

Explanation / Answer

a)

Linear speed = angular speed * distance

Converting from revolutions per minute to miles per hour:

12 rpm ·( 2 r ft/ 1 revolution)· (1 mile / 5280 ft) · (60 minutes / 1 hour) = 250 miles / hour

(12r)/44 miles / hour = 250 miles/hour

(12r)/44 = 250

(12r) = 11000

r = 11000 / (12)

r = 291.93 ft

b) From P to the top of the wheel takes 1.3seconds.

Period= 60/12 seconds (1 revolution)

1.3 sec / (60/12) = .26of a revolution.

If wesubtract ¼ of a revolution from that,

Arc length intersected by .

.26 - .25 = .01 revolution = .01*360 = 3.6 degrees = 0.062 radians

c)

Since from P to the top of the wheel takes 1.3seconds, then from the top of the wheel until Tiff becomes a human missile is 4.6 seconds.

4.6 seconds / (60/12)= .92revolutions.

0.92·360° = 359.08 degrees = 6.26 radians

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.