The problem with almost all physics problems is that it all depends on your frame of reference and your initial conditions. Physics is only absolute in an infinite frame of reference.
Let's suppose you have a truck (or better yet a 'physics sled'- a theoretical cart that moves perfectly smoothly ) moving at 160fps in a straight line. (as a vector +160fps)
Our archer on the sled fires an arrow at 160fps in the exact oposite direction of the movement of of the sled (which means, as a vector the arrow is moving at -160fps)
And let's do it all in a vacuum so there's no aerodynamic effects.
From the frame of reference of the archer, the arrow would fly off the bow at 160fps because the archer and arrow start at 0 speed relative to each other. In fact, if the archer was in a closed box on the physics sled (which moves perfectly smoothly) he would have no reason to believe (and no way to prove) that he was moving at all. It would all be the same as if he was standing on solid ground. (general relativity)
However, in the frame of reference of the ground, we see the walls of the closed box are moving at 160fps on top of the sled.
So, for the arrow to be moving at 160fps relative to the walls of the box as it appears to the archer, the arrow must have 0 velocity in the frame of reference of the ground. If the arrow had any speed at all.. say 20fps relative to the ground.. then the archer would see it moving at 180fps-- which I'm sure would be a nice surprise.
So, from the frame of reference of an observer on the ground, the arrow would stop in space (zero velocity ) and the archer would speed away from it at 160fps.
In the closed box the arrow would slam into the box moving at 160fps. If the arrow didn't hit something solid, the physics sled would move out from under it and eventually it would accellerate under gravity straight to the ground. (having 0 velocity and momentum in the ground's frame of reference)
Of course it wouldn't be quite like that because the arrow does't have infinite accelleration so through part of its flight it will actually be moving slower than 160fps which means, from the ground frame of reference, it will be 'flying backwards' even though from the archer's frame of reference it will be moving clearly away from the bow at all times.
This experiment is easy enough to do in a sciene lab with slower moving objects (which are also less affected by aerodynamics making the vacuum condition less important).
No energy is 'lost' since the moving arrow has kinetic energy in the direction of the sled and the bow adds kinetic energy in the oposite direction doing work to accellerate the arrow in a new direction. (or to DEcelerate the arrow if you're in the ground frame of reference)
The reason none of this looks like it does in real life is because we're ignoring SO many variables like aerodynamic effects--
In theory, if you stand in the box of a moving truck and throw a softball our in front of the truck you should see it fly off ahead of you (truck velocity plus throw velocity). In reality you're going to be going to the dentist because the softball will rapidly decellerate due to air resistance and you'll catch up to it with your teeth. Not pretty. (however, at no point is the softball ever moving 'towards' you in the ground frame of reference
)
Jake
(who just sprained a brain lobe)
Topic: Hypothetical question (Read 7141 times)
