(1) is represented by the known a coordinate (0,3),

AO=3, tan∠ACB= 4/3, so AB=4, so the coordinate of point C is (4,0).

So the analytical formula of AC is y=-3/4*x+3.

(2) Let the coordinate of point D be (x, -3/4*x+3), the intersection point D be the perpendicular to the Y axis, and the vertical foot be f..△ADF∽△ACO, so AD/AC=DF/OC.

AD=3t, AC=5, DF=x, OC=4, and the solution is x= 12t/5, then the coordinate of point D is (12t/5, -9t/5+3).

(3)D moves on AC, so 0≤t≤5/3, and △ODE is a right triangle.

Then DM is perpendicular to the X axis, and the vertical foot is m△DOF∽△DEM.

T= 1 or 45/57.

It's been a long time. Please let me know if you have any questions. Thank you!