A ship is flying away from Earth at 0.9c (where c is the speed of light). A missile is fired that moves toward the Earth at a speed of 0.5c relative to the ship. How fast does the missile move relative to the Earth

the required speed with which the missile move relative to the Earth is -0.727c

Explanation:

Given the data in the question;

relative velocity relation;

u' = u-v / 1 -

so let V represent the velocity as seen by an external reference frame; u=V

and let V represent the speed of the secondary reference frame; v=V

hence, u' is the speed of B as seen by A

so

u' = V-V / 1 -

now, given that; V = 0.9c  and V  = 0.5c

we substitute

u' = ( 0.5c - 0.9c ) / 1 -

u' = ( 0.5c - 0.9c ) / 1 -

u' = ( 0.5c - 0.9c ) / 1 - (0.5 × 0.9)

u' = ( -0.4c ) / 1 - 0.45

u' = -0.4c / 0.55

u' = -0.727c

Therefore, the required speed with which the missile move relative to the Earth is -0.727c

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