first two bits of information
max is 8, min is -8, so a = 8
period = 2?/k = 20 min
20k = 2?
k = ?/10
so let's start with h = 8 sin (?/10)t
so we have the "shape" of our curve
(sketch this from 0 to 20)
http://www.wolframalpha.com/input/?i=h+%3D+8+sin+((%CF%80%2F10)t)
this has a min of -8, but we want our minimum to be 1, so let's add 9
h = 8 sin(?/10)t + 9
http://www.wolframalpha.com/input/?i=h+%3D+8+sin+((%CF%80%2F10)t),h+%3D+8+sin((%CF%80%2F10)t)+%2B+9
notice that this has a min of 1 at t = -5, but we want that min to be at t = 0
so let's "move" our curve 5 units to the right
h = 8 sin( (?/10)(t-5) ) + 9
We could just as well used a cosine curve to do the above. As a matter of fact, Wolfram switched my last equation to a cosine curve
http://www.wolframalpha.com/input/?i=h+%3D+8+sin+((%CF%80%2F10)t),h+%3D+8+sin((%CF%80%2F10)t)+%2B+9,+h+%3D+8+sin(+(%CF%80%2F10)(t-5)+)+%2B+9
the ferris wheel at an amusement park measures 16m in diameter. the wheel does 3 rotations every minute. the bottom of the wheel is 1m above the ground...
a) determine the simplest equation that models Megan's height above that ground(h) over time (t). give 2 more equations that model the situation.
2 answers
I said: period = 2π/k = 20 min
That should have been 20 seconds
That should have been 20 seconds