Question: A red arrow starts at the reference point and points to the upper-left toward about 315° (northwest), with the arrow tip in the top-left region. Position hint: top-left. The arrow in the figure below represents displacement of a tectonic plate. This measurement was taken over 50 years. The arrow is 55 mm in length. What is the azimuth (compass bearing) and instantaneous velocity of plate displacement? Choices are: a. azimuth: 126°, velocity: 1.1 mm/year b. azimuth: 306°, velocity: 0.9 mm/year c. azimuth: 306°, velocity: 1.1 mm/year d. azimuth: 126°, velocity: 0.9 mm/year
1. **State the problem:** We have a displacement arrow of length $55$ mm representing tectonic plate movement over $50$ years. We need to find the azimuth (compass bearing) and the instantaneous velocity of the plate displacement.
2. **Understanding azimuth:** Azimuth is measured clockwise from the north (0°). The arrow points northwest, which corresponds to about $315^\circ$. However, compass bearings are usually given as angles from north clockwise, so $315^\circ$ is the azimuth.
3. **Calculate velocity:** Velocity is displacement divided by time.
$$\text{velocity} = \frac{\text{displacement}}{\text{time}} = \frac{55\text{ mm}}{50\text{ years}} = 1.1\text{ mm/year}$$
4. **Check choices:**
- Azimuth $306^\circ$ is close to northwest but not exactly $315^\circ$.
- Azimuth $126^\circ$ points southeast, opposite direction.
- Velocity $1.1$ mm/year matches our calculation.
5. **Conclusion:** The azimuth is approximately $306^\circ$ (closest to northwest) and velocity is $1.1$ mm/year.
**Final answer:** c. azimuth: $306^\circ$, velocity: $1.1$ mm/year