A ferris wheel has radius of 25 m and its centre is 27 m above the ground. It rotates once every 40 seconds. Sandy gets on the ferris wheel at its lowest point and the wheel starts to rotate.
Determine a sinusodial equation that gives her height, h, above the ground as a function of the elapsed time, t, where h is in metres and t in seconds
all i know is that amplitude is 25
and period is 40
and the vertical displacement is 27
Such an equation is not unique, I thought
h = 25sin π/20(t +30) + 27
when t = 0 , h = 2 , let's say the platform to get on
when t = 10 , h = 27 , that makes sense
when t = 20, h = 52 , at the top, makes sense
when t = 40, h = 2, back down to the start,
looks ok
i don't get where the horizontal displacement of +30 comes from :S
I started with
y = 25sin π/20(t) , sketch that graph
I knew I had to raise it 27 metres
but that the low point or the starting point of the ride at 30 seconds, we wanted that to be at 0 seconds, so I had to move the whole curve 30 seconds to the left.
To determine the sinusoidal equation that relates Sandy's height above the ground, h, as a function of the elapsed time, t, we can use the formula for vertical displacement of a sinusoidal function:
h = A * sin(2π/P * (t - t0)) + C
Where:
- A is the amplitude
- P is the period
- t0 is the horizontal displacement (in this case, the time when Sandy gets on the ferris wheel)
- C is the vertical displacement
Given that the amplitude (A) is 25, the period (P) is 40, and the vertical displacement (C) is 27, we can substitute these values into the equation:
h = 25 * sin(2π/40 * (t - t0)) + 27
Since Sandy gets on the ferris wheel at its lowest point, we know that at t = 0, h = 0. This means that t0 should be 0 as well.
Thus, the final sinusoidal equation that gives Sandy's height, h, above the ground as a function of the elapsed time, t, is:
h = 25 * sin(2π/40 * t) + 27