Answer
$5.07m/s$
Work Step by Step
The speed of the crate can be determined as follows:
$mv_{y_1}+\Sigma \int ^{t_2}_{t_1} F_y dt=mv_{y_2}$
We plug in the known values to obtain:
$10+2\int ^{3}_{0} (100+5t^2)dt-20(9.81)(3)=20v$
$\implies 2(100t+\frac{5}{3}t^3)|^3_{0}-588.6=20v$
This simplifies to:
$v=5.07m/s$
