Answer
The total time is 1.67 seconds.
Work Step by Step
We can find the time $t$ for the bowling pin to reach maximum height. Note that v = 0 m/s at maximum height.
$t = \frac{v-v_0}{a} = \frac{0-8.20~m/s}{-9.80~m/s^2}$
$t = 0.8367~s$
The total time for the bowling pin to reach maximum height and fall back down to the juggler's hand is $2t$.
$2t = (2)(0.8367~s) = 1.67~s$
The total time is 1.67 seconds.
