Assume a bullet travels 99.9% the speed of light fired at a slow moving target.
If an ant was strapped to that bullet, allowing enough distance, from the ants point of view time is moving much slower than that of the target.
From the ants perspective it would see the target moving very fast out of the way.
However to an observer watching the bullet it flew through the air and hit the target before it had time to move.
How can the bullet hit the target from the point of view of the ant?
A bullet is fired from a gun, then it hits a target.
Alice says that the bullet traveled ten miles in one minute. Bob says it traveled twenty miles in two minutes. They can still agree on the speed of the bullet.
They are certainly not going to disagree about whether the target gets hit.
The first point to remember when thinking about special relativity is that if an event happens in one frame it also happens in every other. You cannot have, for example, a situation in which a bullet hits a target in one frame of reference but misses it in the other.
So, let's assume the target is moving east to west and the bullet is moving south to north, and they meet at some point P. Your question is how does this appear to work in the two different frames?
The answer lies in 'the relativity of simultaneity'. Broadly what that means is that in the ground frame of an observer who is performing the experiment, when it is some time t for the observer, it is that time everywhere in the observer's frame- however, it is not that time everywhere in any other frame moving relative to the observer. In the moving frame, time in the observer's frame is out of synch, and the extent to which it is out of synch increases with speed and distance. So if the observer fires the gun at t, they consider the target's position at the start of the experiment to be its position at time t. However, in the frame of the speeding bullet, the position of the target at the start of the experiment is not the same as for the observer. If the target in one frame seems to have more time to move out of the way, then that is compensated for, by the relativity of simultaneity, because the target in that frame starts off further from the point of collision, so the extra time they have is used up in reaching the more distant collision point.
I suspect you will struggle to understand that, because I have never known anyone who has assimilated the implications of the relativity of simultaneity without having to spend a lot of time cogitating on it and re-programming their mind to rid it of the effect of years of having thought of time in a Newtonian way. Nonetheless, it is the answer, and if you want to understand relativity them my recommendation is to start with the relativity of simultaneity, as that is the key to understanding all the other strange phenomena such as time dilation, length contraction and so on.
Let me draw a picture: a linear accelerator (la), accelerates a projectile to velocity V/C =0.999~1, in negligible time (e.g. a nuclear decay), at a target fixed with respect to the la. The observer with the projectile hits the target in time. T =D/(gamma*V) in projectile's rest frame, where D is the distance from emission from the la to the target, and. 1/gamma = sqrt(1-(V/C)^2) is the length contraction factor. The time of flight with respect to the lab (la) is T = D/V. The point of confusion in this scenario is why the ant ages less than the folks back home ... much less at that speed. That's The Twin Paradox. Since V is symmetric between the ant and approaching target and the Target and the approaching ant, why don't the homies age the same as astroant? Astroant was accelerated into a different frame which contracted the Distance.
