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Question

Please help will rate and give points if a correct worked out answer is given

The rogue starship Galaxa is being chased by the battle-cruiser Millenia. The Millenia is catching up to the Galaxa at a rate of 0.650c when the captain of the Millenia decides it is time to fire a missile. First the captain shines a laser range finder to determine the distance to the Galaxa and then he fires a missile that is moving at a speed of 0.435c with respect to the Millenia. What speed does the Galaxa measure for the missile as they both approach the starship? Give answer as multiple of c.

Explanation / Answer

Speed of Millenia wrt to Galaxa, u=0.650c

Speed of missile wrt ti Millenia, v=0.435c

Speed of missile wrt to Galaxa can be measured by relativistic addition

Thus speed of missile wrt Galaxa, w= (u+v)/[1+uv/c2]

=(0.650c+0.435c)/[1+(0.650c*0.435c)/c2]

=1.085c/1.28275

=0.8458c or 0.846c

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