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?
- 六呎將軍Lv 71 十年前最愛解答
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:
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
- 1 十年前
How fast is a rider rising when his seat is 16m above ground level?