Answer
$H=67.5$ m
Work Step by Step
At the highest point, $y=H$, the vertical component of velocity is zero ($v_{y}=0$ )
Use 4-24 to find y=H
$v_{y}^{2}=(v_{0}\sin\theta_{0})^{2}-2g(y-y_{0})$
$0=(v_{0}\sin\theta_{0})^{2}-2gH$
$2gH=(v_{0}\sin\theta_{0})^{2}$
$H=\displaystyle \frac{(v_{0}\sin\theta_{0})^{2}}{2g}$
$H=\displaystyle \frac{(42.0m/s)\sin 60^{o}}{2(9.80m/s^{2})}$
$H=67.5$ m
