The period is π , and the amplitude is 7
so we could go with y = 7sin πt
we want the min to be 0 and the max to be 14
so we need y = 7sin πt + 7
when t = 0 we want y = 0, so we need a phase shift
y = 7sin π(t+Ø) + 7
when t=0, we want y = 0
when t = 1/2 we want y = 7
when t = 1 , we want y = 14
et
so using t=1, y = 14
14 = 7sin π(1+Ø) +7
1 = sin π(1+Ø)
I know that sin π/2 = 1
so π(1+Ø) = π/2
1+ Ø = 1/2
Ø = -1/2
a possible equation:
y = 7 sin π(t - 1/2) + 7 or y = 7 sin (πt - π/2) + 7
checking:
when t = 0 , y = 0
when t = 1/2, y = 7
when t = 1 , y = 14
looks good ....
when t = 18/60 or 3/10
y = 7 sin π(3/10 - 1/2) + 7
= appr 2.89 m
confirmation:
http://www.wolframalpha.com/input/?i=plot+y+%3D+7+sin+(%CF%80x+-+%CF%80%2F2)+%2B+7
Matthew is riding a ferris wheel at a constant speed of 2 revolutions per minute. The boarding height for the wheel is 1m, and the radius is 7m.
a) What is the equation of the function that describes Matthew's Height in (m) in terms of time in minutes, assuming matthew starts at the lowest point of the wheel?
b) Sketch one cycle of the of function
c) What is Matthew's height after 18 minutes?
1 answer
2 answers