Answer
$s=1.90ft$
Work Step by Step
We can determine the required length of the spring as follows:
$\frac{1}{2}mv_1^2+\Sigma U_{1\rightarrow 2}=\frac{1}{2}mv_2^2$
$\frac{1}{2}mv_1^2+\frac{1}{2}k(x_1^2-x_2^2)=\frac{1}{2}mv_2^2$
We plug in the known values to obtain:
$\frac{1}{2}(\frac{4}{32.2})(9)^2+\frac{1}{2}(50)(s-1.5)^2-(s-1.5-0.2)^2=0$
This simplifies to:
$s=1.90ft$
