“If ship is traveling at speed of light, could some light based “radar†bounce off something in ships path, and return echo, faster than ship itself meeting said obstacle?”
No, the maximum speed of light (in a vacuum) is invariant, that is one of the basic rules of relativity. What this means is that, if you were on a spaceship traveling at the speed of light, and you turn on the headlights (or the radar beam in your example), the beam wouldn’t go anywhere.
When we think of physical objects, like standing on a moving train and throwing a ball forward, we have to add the velocity of the train and the ball together to get the total velocity. With light, it just doesn’t work that way. It has a maximum speed, and it can never travel faster than that, period.
Now, the whole question really is academic, because if you were traveling on a ship at the speed of light, time would stop. So you couldn’t possibly turn on the radar or headlights, because you wouldn’t be able to move, or think, or anything else. You’d be frozen in time. If the ship ever decelerated below light speed, it would seem to you as if you had traveled instantaneously.
Thanks everyone who answered my question. These concepts fascinate me!