Answer
The highest tree the ball could clear is $30.2\text{ m}$ tall.
Work Step by Step
We know that
$y_{max}=\frac{v_{\circ}^2sin^2\theta}{2g}$
We plug in the known values to obtain:
$y_{max}=\frac{(34.4m/s)^2(sin 45^{\circ})^2}{2(9.8m/s^2)}$
$y_{max}=30.2m$
