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mel-nik [20]
3 years ago
10

Ron is on a Ferris wheel of radius 30 ft that turns counterclockwise at a rate of one revolution every 12 seconds. The lowest po

int of the Ferris wheel​ (6 o'clock) is 15 feet above ground level at the point​ (0,15​) on a rectangular coordinate system. Find parametric equations of Ron as a function of time t​ (in seconds) if the Ferris wheel starts​ (t=​0) with Ron at the point ​(30​,45​).
Physics
1 answer:
alexgriva [62]3 years ago
7 0

Answer:

x = 30cos\frac{\pi}{6}t

y = 30sin\frac{\pi}{6}t + 45

Explanation:

1 full revolution is 2\pi. let \theta be the angle of Ron's position.

At t = 0. \theta = 0

one full revolution occurs in 12 sec, so his angle at t time is

\theta =2\pi \frac{t}{12} = \frac{\pi}{6}t

r is radius of circle and it is given as

x = rcos\theta

y = rsin\theta

for r = 30 sec

x = 30cos\frac{\pi}{6}t

y = 30sin\frac{\pi}{6}t

however, that is centered at (0,0) and the positioned at time t = 0 is (30,0). it is need to shift so that the start position is (30,45). it can be done by adding to y

x = 30cos\frac{\pi}{6}t

y = 30sin\frac{\pi}{6}t + 45

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