A pebble is wedged in the bottom of a tire.
The horizontal distance of the pebble from the left-most edge of the tire varies
sinusoidally with the distance the wheel has traveled. The diameter is inches.
= distance of the pebble from the leftmost edge of the tire.
= horizontal displacement of the wheel.
(a) Write an equation relating and
(b) Determine the first positive value that makesLet the radius beCode:* * * * * * * * * * E O * D *-+-------* * * : / | * : / θ | *: / | * C* - - - +A * * | * - - - - - * * * - - - - - - B
When the wheel has turned radians,
. . it has moved a distance equal to arc(BC): . .
We see that: .
. . Hence: . .
Substitute  into : .
Since . we have: . .(a)
If , we have: .
Therefore: . .(b)