Answer
$t = 0.00417~s$
Work Step by Step
$V = 163~sin(\omega~t)$
The value of $V$ will be a maximum when $sin(\omega~t) = 1$, which first occurs when $\omega~t = \frac{\pi}{2}$
We can find the least positive value of $t$:
$\omega~t = \frac{\pi}{2}$
$t = \frac{\pi}{2~\omega}$
$t = \frac{\pi}{(2)(120~\pi)}$
$t = \frac{1}{240}$
$t = 0.00417~s$
