1. ## Trig

A bicycle wheel has a diameter of 60cm. The bike moves at a speed of 6 m/s.
a) The outside of the tire has a speck of paint on it. Determine an equation for the height, h meters, of the speck above the road as a function of time, t seconds. assume the speck is at its lowest point (h=0) when t=0

Thanks

2. Originally Posted by meli3000
A bicycle wheel has a diameter of 60cm. The bike moves at a speed of 6 m/s.
a) The outside of the tire has a speck of paint on it. Determine an equation for the height, h meters, of the speck above the road as a function of time, t seconds. assume the speck is at its lowest point (h=0) when t=0

Thanks
The formula to relate linear and angular velocity is

$v=\omega \cdot r$ where omega is the angular velocity and r is the raduis of the circle so solving for omega we get

$\omega=\frac{v}{r}=\frac{6 m/s}{.03m}=\frac{200 radians}{s}$

Since we want the wave to start at its lowest point we will use the cosine function but cos(0)=1 so we will reflect it accross the x-axis and use -cos(0)=-1 or -cos(x) Since the radius of the tire is 30cm we need the amplitude of the wave to be 30cm and we need to shift it up 30cm as well so we get

$f(x)=-30\cos(\text{something})+30$

We can use the angular velocity found in the beginning for something to get

$f(x)=-30\cos(200x)+30$

I hope this helps.

Good luck.