Chapter 1.5, Problem 1bT

The picture of the spaceships and shuttle from the previous page is reproduced at right.

The diagram below the picture shows the positions of the two spaceships and the shuttle at time $t_i$ in the reference frame of spaceships A.

Diagram for reference frame of spaceships A

Sketch spaceships A, B, and the shuttle at their positions at time $t_t$ as measured in the reference frame of spaceships A.

In the box at right, draw and labelvectors for ${\stackrel{\to }{x}}_{S,A}^{(i)},{\stackrel{\to }{x}}_{S,A}^{(f)},\text{and}\Delta {\stackrel{\to }{x}}_{S,A}$ .

${\stackrel{\to }{x}}_S^{(i)},{\stackrel{\to }{x}}_S^{(f)},\text{and}\Delta {\stackrel{\to }{x}}_S$ in frame of spaceship A

Describe how you could use $\Delta {\stackrel{\to }{x}}_{S,A}$ to determine the velocity of the shuttle in the frame of spaceship A.

Is the magnitude of the velocity of the shuttle in the frame of spaceship A greater than, less than, or equal to the magnitude of the velocity of the shuttle in the frame of spaceship B? Explain.