There is a red dot on the outer edge of a wheel. The wheel is rolling on the ground in a counterclockwise direction and has diameter 13 inches. Which of the following is a formula using the sine function for the height of the dot above ground level after $t$ seconds if the wheel completes one full revolution every 2 seconds. At $t=0$ the dot in 9 o'clock position.
A) $\frac{13}{2}+\frac{13}{2} \sin (\pi+\pi t)$
B) $\frac{13}{2} \sin (\pi+\pi t)$
C) $\frac{13}{2}+\frac{13}{2} \sin (\pi t)$
D) $\frac{13}{2}+\frac{13}{2} \sin (\pi+t)$

Question

Quizplus · Accepted Answer

The wheel completes one revolution every 2 seconds, so the angular speed is $\pi$ radians per second. At $t=0$, the dot is at the 9 o'clock position, which corresponds to $\pi$ radians. The height of the dot is given by the vertical component of its position, which is $\frac{13}{2} + \frac{13}{2} \sin(\pi + \pi t)$.

There Is a Red Dot on the Outer Edge of a Wheel