Differentials 急

Question

A Ferris wheel with a radius of 10m is rotating at a rate of one revolution every 2 minutes. How fast is a rider rising when his seat is 16m above ground level?

Answer 1

最愛解答

First of all, the angular velocity of the wheel is 2π/(2 x 60) = π/60 rad/s

So, with ref. to the diagram below:

圖片參考：http://i388.photobucket.com/albums/oo325/loyitak19...

We have:

dθ/dt = π/60

Also at this moment: sin θ = 3/5 and hence θ = 4/5

Suppose that the vertical height is h, it is given by:

h = 10 + 10 sin θ

dh/dt = 10 cos θ (dθ/dt)

= 10 x 4/5 x π/60

= 2π/15 m/s

2010-09-16 08:26:30 補充：

dh/dt id already indicating the answer to the question "How fast is a rider rising when his seat is 16m above ground level?"

Moreover, the 6 m in the figure is referring to the vertical height of the rider above the centre of the wheel.

資料來源： Myself

Answer 2

How fast is a rider rising when his seat is 16m above ground level?

咁呢個去左邊呀?? 多謝幫助