Diameter of the wheel is 25-1=24m. When t=0 y=1.5m. Angular speed is 540 degrees (1.5*360) per minute or 9 degrees per second. A complete revolution is 360 degrees so it takes 40 seconds for one revolution. When t=0 and t=40 the trig function will have the same value.
The minimum value of sin or cos is -1 and the maximum is 1. The difference between max and min has to be 24m.
Assume the first option is y=13sin(...)-12 rather than y=13sin(...)=12and the others are as shown, we have:
- ±13-12=-25 to 1 as the range - eliminate option1
- ±12+13=1 to 25 possible option
- Ditto
- Ditto
- Eliminate option5 because range would be 14 to 38, and 38 is higher than the wheel
- Possible option
The trig function must have the same value for t=0 and 40:
- Option1 already eliminated
- Same value for t=0 and 40
- Ditto
- Different value for t=0 and 40-eliminate option4
- Option5 already eliminated
- Possible option
The only options left are 2, 3 and 6. Minimum is t=0 and maximum is t=20 (highest point):
Option 2 min: 1.48; max: 24.52
Option 3 min: 1.48; max: 24.52
Option 6 min: 1.48; max: 24.52. So these options provide reasonable models for the height of the platform.
The three curves have identical periods and amplitudes. The only difference is that they are phase-shifted with respect to one another. The factor of 9 degrees per second in the arguments confirms this. The time base, t, for each of them has a different reference point: -1.8, 11.8 and 38.2 seconds (38.2-(-1.8)=40 seconds, the cycle time). For options 2 and 6 only the value of y, the height of the platform is 1.5m (approximately); at t=0, option 3 is at the maximum platform height of about 24.5m (the average of 38.2 and -1.8), corresponding to the lowest point of about 1.5m for options 2 and 6. The reverse is true at t=20.