Answer
$4.03m/s$, $725J$
Work Step by Step
We can determine the required speed and the work done as follows:
According to the principle of conservation of angular momentum
$mr_1v_1=mrv_t$
$\implies v_t=\frac{r_1v_1}{r}$
$\implies v_t=\frac{8(3)}{6}=4m/s$
Now, $v=\sqrt{v_t^2+v_r^2}$
We plug in the known values to obtain:
$v=\sqrt{16+0.25}=4.03m/s$
The work done can be calculated as
$W=\frac{mv_2^2}{2}-\frac{mv_1^2}{2}$
$\implies W=\frac{m}{2}(v_2^2-v_1^2)$
We plug in the known values to obtain:
$W=\frac{200}{2}(16.25-9)$
This simplifies to:
$W=725J$
