Sure. I used one equation of motion (variables: u is starting velocity, s is displacement, a is acceleration and t is time taken):
s = ut + 0.5 at^2
By setting the arrow time of flight to a constant and known value, it becomes easy to figure out the missing variables. This does not necessarily reflect reality, but it's more than good enough for a game. For movement in the x direction, I chose to make the movement linear in all screen directions ie constant x velocity and zero acceleration. Thus the equation becomes u = s / t.
For movement in the y direction (ie vertical) I had to consider gravity acceleration. The variable s is the difference between start and end y values. Starting velocity is then figured by manipulating the equation to give u = (s - 0.5 at^2 ) / t. All of the variables s, a and t are known, so the starting vertical velocity can be figured out. That leaves moving the arrows, which is done every tick by giving each arrow object an object variable Y_Vel (for y velocity)... et voila!