Question

Hello.. In your previous solution to the question:
"Dave is going for a ride on his unicycle. The radius of the wheel is 25.5cm. When he gets on, the valve of the wheel is at its maximum height. He pedals along a path at a speed of 30km/h.

At what height will the valve be located after he has cycled for 4 minutes?

How do I find the period of this? I think try finding the equation first. Thanks!"


or ....
amplitude is 25.5

for period:
need time for one rotation
length of one rotation = 51π (see above)
speed = 50,000 cm/min
time for one rotation = dist/speed
= 51π/50000

we know the equation must be something like
Height = 25.5cos kt + 25.5

where 2π/k =51π/50000
k = 100,000/51

height = 25.5 cos ((100,000/51)t) + 25.5
set calculator to radians, sub t = 4
to get
height = 21.659

argghh, small discrepancy in answer.
(can't seem to find my error)
-------------------------------

Since h(t)=a cos(b(x-c))+d
Shouldn't the amplitude (a) be calculated by (max - min)/2 and the (d) is calculated by (max + min)/2?

Answer 1

C = pi * D = 3.14 * 2*25.5 = 160.14 cm.
= 1.614 m = Circumference.

V = 30km/h = 30,000m / 60min=500 m/min.

d = 500m/min * 4min = 2000 m.

2000m / 1.614m/rev =1239.157373 revolutions.

A = 90 + 0.157373*90 = 104.2 Deg.
h = 25.5 + 25.5*sin104.2 = 50.2 cm.