A yo-yo is a child’s toy that spins along a string attached to the center axle of two disks. Suppose a certain child releases the yo-yo from a height of 2 feet with the toy winding itself back into the child's hand, taking the same amount of time to go up, as it did to go down. After 4.9 seconds of the child playing, the yo-yo is at the end of the string 3.5 inches off the ground, and after 6.86 seconds the yo-yo is once again at the end of the string.

a. What is the length of the string?

b. How long does it take the child to release and then catch the yo-yo again?

c. Assume the height of the yo-yo from the ground varies sinusoidally with time. Sketch a graph of a complete yo-yo cycle. Label both axis, midline, and all critical points on the graph.

d. Write an equation expressing the height of the yo-yo, h(t)h(t) from the ground in terms of the time, tt, where t=0 represents the first time the child started paying.

e. How far off the ground was the yo-yo after 1.25 seconds of the child paying? Was the yo-yo rising or falling? How much string is currently unwound?

f. When was the first time the yo-yo was a foot off the ground?

g. Describe a reasonable domain for this situation.