## College Physics (4th Edition)

The speed of the ship that passed you according to Earth observers is $0.97~c$
Let $v_{AE}$ be the velocity of ship A (our ship) relative to Earth. Then $v_{AE} = 0.90~c$ Let $v_{BA}$ be the velocity of ship B (the other ship) relative to ship A. Then $v_{BA} = 0.50~c$ We can find $v_{BE}$: $v_{BE} = \frac{V_{BA}~+~v_{AE}}{1+\frac{(v_{BA})~(v_{AE})}{c^2}}$ $v_{BE} = \frac{(0.50~c)~+~(0.90~c)}{1+\frac{(0.50~c)~(0.90~c)}{c^2}}$ $v_{BE} = \frac{1.40~c}{1.45}$ $v_{BE} = 0.97~c$ The velocity of ship B relative to the Earth is $0.97~c$ Therefore, the speed of ship B relative to the Earth is $0.97~c$