Final answer:
In special relativity, the velocity at which a canister must be shot from the first ship to approach another at 0.999c, considering the ships are moving towards each other at 0.800c, is calculated using the relativistic velocity addition formula. The result is option (c) 0.800c, illustrating the non-intuitive nature of relativistic velocity additions.
Step-by-step explanation:
The question pertains to special relativity and the addition of velocities. To determine the velocity at which a canister must be shot from the first ship to approach another ship at 0.999c, as seen by the second ship, we have to use the relativistic velocity addition formula:
v = (v1 + v2) / (1 + (v1*v2/c^2)),
where v is the resultant velocity, v1 is the velocity of the canister relative to the first ship, v2 is the velocity of the first ship relative to the second ship, and c is the speed of light. Using the provided information where two ships are heading towards each other at a relative speed of 0.800c, and we need the canister to approach at 0.999c relative to the second ship, we can solve for v1.
Substituting the known values into the equation:
v1 = (v - v2) / (1 - (v*v2/c^2)),
After calculations, we find that the speed at which the canister must be shot from the first ship is answer option (c) 0.800c. This is a counter-intuitive result of relativistic speeds, where adding velocities does not simply follow classical mechanics but must account for the effects of relativity.