Question

In Fig. 37-36, two cruisers fly toward a space station. Relative to the station, cruiser A has speed 0.800c. Relative to the station, what speed is required of cruiser B such that its pilot sees A and the station approach B at the same speed?

Short answer

The speed of cruiser B such that cruiser A and station approaches it with same speed is $0.400c$.

Step-by-step solution

Identification of given data

The relative speed of Cruiser A is $v_A=0.800c$

The relative speed of cruiser A relative to B will be equal to the relative speed of cruiser B relative to station. The station is stationary so its speed will be zero relative to both cruisers.

Determination of speed of cruiser B

The speed of cruiser B is given as:

$$\begin{gathered} v_s-v_B=v_B-v_A \\ {v}_B=\frac{v_s+v_A}{2} \end{gathered}$$

Here, $v_s$ is the speed of station and its value is zero because both cruisers are at rest.

Substitute all the values in the above equation.

$$\begin{gathered} v_B=\frac{0+0.800c}{2} \\ {v}_B=0.400c \end{gathered}$$

Therefore, the speed of cruiser B such that cruiser A and station approaches it with same speed is $0.400c$.