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Leading up to an epic battle, observers on Earth see two enemy spaceships approa

ID: 1769156 • Letter: L

Question

Leading up to an epic battle, observers on Earth see two enemy spaceships approaching from opposite directions: a Romulan ship is approaching at a speed of 0.82c from one direction, while a Klingon ship is approaching at a speed of 0.88c from the exact opposite direction.

(a) What is the speed of the Romulan ship as seen by the Klingons in their reference frame?
(b) The Klingons fire a missile at the Earth, which observers on Earth see approaching at 0.98?? . What is the speed of the missile as seen by the Klingons in their reference frame?
(c) Human defenders fire a powerful laser pulse at the Klingon ship. The pulse leaves the Earth at a speed of ??, of course. As the laser pulse approaches the Klingon ship, what is its speed as seen by the Klingons in their reference frame?

Explanation / Answer

The relativistic velocity addition relation is

S = (U + V)/[1+(UV/C^2)]

where U and V are the speeds of objects 1 and 2 in the rest frame

and S is the speed of 1 in the moving frame of 2.

The convention used is that if both 1 and 2 are approaching each other both U and V are positive.

a) U =+0.82C , V =+0.88C

S =(0.82+0.88)*C/(1+0.82*0.88) =0.987C

b) U =0.98C V= -0.88C

S =(0.98-0.88)*C/(1+0.88*0.98) =0.0537*C

c) The speed of light is the same in all reference systems. Thus the speed of laser in the reference frame of Klingons will still be C.