It is a non-problem.
If we want to stay within limits of science: edit: and engineering
- It will be extremely hard to accelerate to 0.75SL and then decelerate to 0. Fuel would need to be like 99.999% of the weight of the rocket, even with stages. So expect to travel at 5-10% of SL.
- It will be extremely hard to shoot any bullets forward, to destroy any objects, again because of relativistic physics, because they would be moving extremely fast relative to our ship.
- And of course shooting anything forward to destroy obstacles slows you down. Newton's laws apply for relativistic travel too.
The only way to travel within the limits of physics as we know it now is to travel slowly, in multi-generation ship, of some hibernation. At such speed, detecting obstacles is simpler, and you have more time to eliminate them by laser (which has less impact on your forward momentum than shooting a bullet to destroy such object).
Of course it is less fun to travel that slowly.
Another option is to discover new physical approach. Like discontinuous jumps in hyperspace, but those are not within limits of laws of physics.
If you want to stick within laws of physics to solve this - you will not be able to get to such speed, and if you ignore physics, you can hyperjump or tractor-beam obstacles or whatever your imagination wants.
Edit: numbers provided by relativistic rocket
- to get to Vega (27 ly) and stop there, we need 57kg of fuel for every kg of payload, using 100% effective engine.
See also http://en.wikipedia.org/wiki/Space_travel_using_constant_acceleration
- Soda can is 94% fuel, 6% of construction. Build structures capable to withstand such forces and cary huge amounts of fual is very hard - read The Tyranny of the Rocket Equation
That's why I argue it is not feasible to travel at such speeds (within limits of physics and engineering as we know it today) so you don't need protection for such speeds. And I agree that it is less fun than zoom around like in Hollywood movies. Tough beans.
In other words: when we will have (now unknown) technology and engineering capable of building such ships, protecting them would be relatively simple task. That's why I say it is a non-problem.
- if rocket will not carry fuel/reaction mass with it, where it will come from? From empty space? Or it will be powered by magic? Wishful thinking cannot power a space ship.
- Of course shooting at rest and at 0.7c follow the same laws - that what EXACTLY theory of relativity says. Problem is the lead time. At 0.7c, universe looks "length contracted" so distant object are closer. And they are coming at you at 0.7c speed, so even if you hit target, you have good chance to get hit by debris, because it is not much time to disperse.
- rifle recoil does not "seems" to slow locomotive because of difference between mass (and inertia) of rifle and train. But Newton's laws still apply, action = reaction force. Anyone who believes that there is no effect on train by shooting rifle from train, cannot expect his opinion about physics be taken seriously.
Physics continues to work, even if some people prefer downvote my answer when I remind them inconvenient facts.
Edit: length contraction - that's cool part about relativity:
- in spaceship: ship length remains same, universe contracts.
- for external observer: distances in universe remain same, ship contracts.