Two softballs, each with a mass of 0.125 kg, are separated by a distance of 820 m in outer space.
a. If the balls are released from rest, what speed do they have when their separation has decreased to 680 m? Ignore the gravitational effects from any other objects.
Hold one ball fixed (a virtual fixed).
work the other ball does
work=integral F dx= G.125^2/r^2 dr from 820 to 680
work= -G*.125^2 (1/820-1/680)
figure that out. But we know in the real world, both balls moved, so divide that work by 2 to get the work done on each ball, and that is equal to the KE of each ball.
From KE, get the velocity.