Question

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

Answer 1

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

Step-by-step explanation:

Given the data in the question;

relative velocity relation;

u' = u-v / 1 -
`(uv)/(c^2)`

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

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

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

so

u' = V
`_B`-V
`_A` / 1 -
`(V_BV_A)/(c^2)`

now, given that; V
`_A` = 0.9c and V
`_B` = 0.5c

we substitute

u' = ( 0.5c - 0.9c ) / 1 -
`((0.5c)(0.9c))/(c^2)`

u' = ( 0.5c - 0.9c ) / 1 -
`(c^2(0.5)(0.9))/(c^2)`

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