Imagine two boats. One travels $5.0 \mathrm{~m} / \mathrm{s}$ eastward relative to the earth and the other $3.4 \mathrm{~m} / \mathrm{s}$ eastward relative to the earth. We set up a reference frame on each boat with the $x$ axis pointing eastward, and choose the first boat (arbitrarily) to be the Home Frame. The second boat is thus the Other Frame. What is the sign of $\beta$, according to the convention established in this chapter?
A) Positive
B) Negative
C) We are free to choose either sign.

Question

Quizplus · Accepted Answer

The sign of $\beta$ is negative because the Other Frame (second boat) is moving eastward at a slower speed (3.4 m/s) relative to the Home Frame (first boat), which means in the Home Frame's perspective, the Other Frame is moving westward or in the negative direction of the x-axis.

Imagine Two Boats 5.0 m/s5.0 \mathrm{~m} / \mathrm{s}5.0 m/s Eastward Relative to the Earth and the Other

Imagine Two Boats $5.0 \mathrm{~m} / \mathrm{s}$ Eastward Relative to the Earth and the Other