#### Answer

(a) At $t = 376.8~s$, the jogger's velocity is $3.0~m/s$ toward the east.
(b) At $t = 94.2~s$, the jogger's velocity is $3.0~m/s$ toward the west.

#### Work Step by Step

(a) We can find the jogger's speed:
$v = \frac{d}{t} = \frac{(2\pi)(90.0~m)}{188.4~s} = 3.0~m/s$
At $t = 376.8~s$, the jogger will be completing the second revolution, so the direction will be the same as the direction at $t=0$. Therefore, at $t = 376.8~s$, the jogger's velocity is $3.0~m/s$ toward the east.
(b) At $t = 94.2~s$, the jogger will be halfway through the first revolution, so the direction will be the opposite as the direction at $t=0$. Therefore, at $t = 94.2~s$, the jogger's velocity is $3.0~m/s$ toward the west.