Answer
$v=3.33m/s$
Work Step by Step
We can determine the required speed as follows:
According to the principle of angular impulse and momentum
$\Sigma H_{z_1}+\Sigma \int_{t_1}^{t_2}M_z dt=H_{z2}$
We plug in the known values to obtain:
$0+\int_0^5 30t^dt+in_0^5 15t(4)dt=150v(4)$
This simplifies to:
$v=3.33m/s$
