Imagine this: an automatic sniper scope [in form of a cross on the screen] is following the moving object [platform]. The scope is getting closer to it and in given time it will reach the object and shot can be fired. This can be achieved by simple decreasing the distance in relation to moving object. But how to apply inertia to it, when the object decides to suddenly change direction? The preferable result would be that scope will still continue to follow the previous direction of objects movement for a short time and then again follow the object while reducing the distance.
In other words - the object and the scope are connected by invisible rubber band which shortens in given time...
Is it possible to achieve this without using the physics?