A racer can cycle around a circular loop at the rate of 3 revolutions per hour. Another cyclist can cycle the same loop at the rate of 5 revolutions per hour. If they start at the same time (t=0), at what first time are they farthest apart?
A racer can cycle around a circular loop at the rate of 3 revolutions per hour. Another cyclist can cycle the same loop at the rate of 5 revolutions per hour. If they start at the same time (t=0), at what first time are they farthest apart?
$\displaystyle s = r \cdot \theta$
for cyclist 1, $\displaystyle \theta_1 = 6\pi t$
for cyclist 2, $\displaystyle \theta_2 = 10\pi t$
$\displaystyle s_2 - s_1 = r(10\pi t - 6\pi t) = r(4\pi t)$
farthest distance will be when they are half a circumference apart ($\displaystyle \pi r$) ...
$\displaystyle t = \frac{1}{4}$ hr