## College Physics (4th Edition)

The speed of of Alpha relative to Bravo is $0.97~c$
Let $L$ be an observer in a stationary lab. Let $v_{AL}$ be the velocity of Alpha relative to the lab. Then $v_{AL} = 0.90~c$ Let $v_{BL}$ be the velocity of Bravo relative to the lab. Then $v_{BL} = -0.60~c$. Then $v_{LB} = 0.60~c$ We can find $v_{AB}$: $v_{AB} = \frac{v_{AL}~+~v_{LB}}{1+\frac{(v_{AL})~(v_{LB})}{c^2}}$ $v_{AB} = \frac{(0.90~c)~+~(0.60~c)}{1+\frac{(0.90~c)~(0.60~c)}{c^2}}$ $v_{AB} = \frac{1.50~c}{1.54}$ $v_{AB} = 0.97~c$ The velocity of Alpha relative to Bravo is $0.97~c$ Therefore, the speed of of Alpha relative to Bravo is $0.97~c$.