Question

the question is "Joe rode his bike over a piece of gum. Joe continued riding his bike at a constant rate. At time t=1.25 seconds the gum was at a maximum height above the ground and 1 second later the gum was at a minimum. If the wheel diameter is 68cm find a trigonometric equation that will find the height in centimeters at any time t.

Answer 1

assuming that at t = 0 the height was zero (at ground level)
Let's use a sine curve.
The amplitude is 34 and the period is 2.5 seconds
2.5 = 2π/k
k = π/1.25

so our basic curve is
h = 34sin(πt/1.25)

We need to raise this 34 cm so it doesn't go below road level
h = 34sin((π/1.25)t) + 34

This does not give us a height of 0 when t = 0, we have to move the curve 1/4 period to the right

h = 34sin((π/1.25)(t - .625)) + 34

testing:
when t = 0 , h = 0 , good!
when t = 1.25, h = 68 , good!
My equation is correct.