Answer
$v_2=1.68m/s$
Work Step by Step
We can determine the required speed as follows:
According to the conservation of energy equation
$T_1+V_1=T_2+V_2$
$\implies \frac{1}{2}mv_1^2+mgh_1+\frac{1}{2}ks_1^2=\frac{1}{2}mv_2^2+mgh_2+\frac{1}{2}ks_2^2$
We plug in the known values to obtain:
$0+(10)(9.81)(0.45)+\frac{1}{2}(500)(0.2)^2=\frac{1}{2}v_2^2+\frac{1}{2}(500)(0.3)^2$
This simplifies to:
$v_2=1.68m/s$
