How fast was the arrow shot?
Hint: In this question, you do not need to know the initial y-position of the arrow, nor should you assume a value. . The final direction of the arrow indicates the ratio of the v_y/v_x. So tan(final_angle with respect to the x-axis)= v_y/v_x but neither v_y, nor v_x are known. Since the arrow initially was fired horizontally, it only has an x component of velocity at first, and since there is no acceleration in x, v_x final= v_x initial. So you only need to find v_x final to get the initial velocity. You need another equation that relates v_y and v_x. Well, v_y = -gt and you can get t from v_x*t=(displacement in x). Use the last two equation to eliminate t, which is not required for this problem, which give another equation that involves v_y and v_x.