I can't figure out how to do these math questions : / Please help
A ferris wheel has a diameter of 22m, and is 1m higher than the ground at its lowest point. The wheel completes one revolution every 15 minutes.
A. Write a sine equation h(t) representing the height a chair is off the ground in meters, as a function of time in minutes, if the chair starts at the highest point.
B. From a height of 18 m or higher, you can see your grandmother's house. For how long each revolution can you see you grandmothers house? (Estimate using a graph of h(t) or g(t))
A ferris wheel has a diameter of 22m, and is 1m higher than the ground at its lowest point. The wheel completes one revolution every 15 minutes.
A. Write a sine equation h(t) representing the height a chair is off the ground in meters, as a function of time in minutes, if the chair starts at the highest point.
B. From a height of 18 m or higher, you can see your grandmother's house. For how long each revolution can you see you grandmothers house? (Estimate using a graph of h(t) or g(t))
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On the (x-y) plane, the height of a rotating circle that starts at (1,0) and rotates about the origin is given by a sin() function sin[((2*pi)/P)*t]. But if we are starting at the point on top (i.e., (0,1)) we can use the cosine function.
Suppose the middle of the ferris wheel is at the origin. Then its height as a function of time would be:
height if middle is at origin = 11*cos[((2*pi)/15)*t], where t is in units of minutes.
This varies between 11 and -11. So lets add 12 to make its middle consistent with the problem:
h(t) = 12 + 11*cos[((2*pi)/15)*t]
For part B, you just need to find the times for which h(t) >= 18. This amounts to solving for when the cosine function is greater than 6/11. You can perhaps use the inverse cosine function on your calculator, making sure to draw the picture to appropriately normalize and interpret the answer.
Suppose the middle of the ferris wheel is at the origin. Then its height as a function of time would be:
height if middle is at origin = 11*cos[((2*pi)/15)*t], where t is in units of minutes.
This varies between 11 and -11. So lets add 12 to make its middle consistent with the problem:
h(t) = 12 + 11*cos[((2*pi)/15)*t]
For part B, you just need to find the times for which h(t) >= 18. This amounts to solving for when the cosine function is greater than 6/11. You can perhaps use the inverse cosine function on your calculator, making sure to draw the picture to appropriately normalize and interpret the answer.