Answer
The speed of each mass will be 1.97 m/s, and they will be moving in opposite directions.
Work Step by Step
By conservation of momentum, since the two objects have the same mass, they will have the same speed after leaving the spring. The total kinetic energy of the masses will be equal to the initial potential energy in the spring.
$K_{total} = U_s$
$\frac{1}{2}mv^2+\frac{1}{2}mv^2 = \frac{1}{2}kx^2$
$2mv^2 = kx^2$
$v^2 = \frac{kx^2}{2m}$
$v = \sqrt{\frac{kx^2}{2m}}$
$v = \sqrt{\frac{(175~N/m)(0.200~m)^2}{(2)(0.900~kg)}}$
$v = 1.97~m/s$
The speed of each mass will be 1.97 m/s, and they will be moving in opposite directions.
