Marcia uses a bow to shoot an arrow with initial velocity of magnitude v0 and at an angle of theta above the?

Question

horizontal. when teh arrow returns to the same height from which is started,

Answer 1

I believe you are asking what will be the final velocity and magnitude of the arrow at the same height downrange. If that is what you are asking the arrow will have the same velocity as when it started but its direction will be theta below the horizontal.

Answer 2

If my rusty Physics is right, the trajectory curve is a symmetrical parabola, so the angle at the position from which the arrow was launched should be theta also.