2. A Ferris wheel with a radius of?m makes one complete revolution every 16 s.The bottom of the wheel is 1.5 m above the ground. a) Draw a graph to show how a person's height above the ground varies with time for three revolutions, starting when the person gets onto the Ferris wheel at its lowest point.Find an equation for the graph. b) How might the graph and the equation change If the Ferris wheel turns more slowly? c) How might the graph and the equation change if the Ferris wheel were larger? higher off the ground? C

**2. Ferris Wheel Problem**<br /><br />**a) Graph and Equation:**<br /><br />Since the problem doesn't specify the radius, let's assume the radius of the Ferris wheel is *r* meters.<br /><br />* **Lowest point:** The bottom of the wheel is 1.5m above the ground. So, the lowest point a person can be is 1.5m.<br />* **Highest point:** The diameter of the wheel is 2*r, so the highest point a person can reach is 1.5m + 2*r.<br />* **Midpoint:** The center of the wheel is at a height of 1.5m + r.<br />* **Period:** The wheel completes one revolution every 16 seconds. This is the period of the function.<br /><br />The graph will be a sinusoidal curve (a cosine curve, specifically, since we start at the lowest point). It will oscillate between 1.5m and 1.5m + 2*r, with a period of 16 seconds.<br /><br />To draw the graph:<br /><br />1. Label the horizontal axis (time) from 0 to 48 seconds (for three revolutions).<br />2. Label the vertical axis (height) from 0 to a value slightly larger than 1.5 + 2*r.<br />3. Mark the lowest point at (0, 1.5).<br />4. Mark the highest point at (8, 1.5 + 2*r).<br />5. Mark the midpoint at (4, 1.5 + r) and (12, 1.5 + r).<br />6. Draw a smooth cosine curve through these points, repeating the pattern for three cycles.<br /><br />The equation for the graph is:<br /><br />h(t) = -r*cos((2π/16)t) + (1.5 + r)<br /><br />where:<br /><br />* h(t) is the height above the ground at time t<br />* r is the radius of the Ferris wheel<br />* t is the time in seconds<br /><br />**b) Slower Rotation:**<br /><br />If the Ferris wheel turns more slowly, the period of the function will increase. This means the horizontal distance between the peaks and troughs of the graph will be greater. The equation will change as follows:<br /><br />h(t) = -r*cos((2π/T)t) + (1.5 + r)<br /><br />where T is the new, longer period.<br /><br />**c) Larger Wheel, Higher Off the Ground:**<br /><br />* **Larger Wheel (Larger radius):** If the Ferris wheel is larger (larger radius), the amplitude of the graph will increase. The highest and lowest points of the graph will be further apart. The equation will change by having a larger value for *r*.<br /><br />* **Higher Off the Ground:** If the Ferris wheel is higher off the ground, the entire graph will be shifted vertically upwards. The lowest point will be higher than 1.5m. The equation will change by adding a constant to the entire function:<br /><br />h(t) = -r*cos((2π/16)t) + (h + r)<br /><br />where 'h' is the new height of the bottom of the wheel above the ground.<br /><br /><br />**Important Note:** Remember to replace *r* with the actual radius given in the problem (if provided) to get the specific graph and equation. Without a specific radius, the solution remains generalized.<br />