Draw a diagram for the following situations. Calculate the distance and displacement in each of the following situations. Include a direction (example: north or northwest) with your answer. 1. Amy runs 2 miles south, then turns around and runs 3 miles north 2. Jermaine runs exactly 2 laps around a 400 meter track 3. Derrick crawls 4 feet south, and then turns east and crawls 6 feet.

Let's analyze each situation step by step, calculate the distance and displacement, and include directions. ### 1. Amy's Run - **Path**: Amy runs 2 miles south, then turns around and runs 3 miles north. - **Distance**: - 2 miles (south) + 3 miles (north) = 5 miles - **Displacement**: - She ends up 1 mile north of her starting point (3 miles north - 2 miles south). - **Displacement**: 1 mile north ### Diagram for Amy: ``` Starting Point | | (2 miles south) | v (A) --------------------> (B) | (3 miles north) | ^ ``` - **Distance**: 5 miles - **Displacement**: 1 mile north --- ### 2. Jermaine's Run - **Path**: Jermaine runs exactly 2 laps around a 400-meter track. - **Distance**: - 2 laps × 400 meters/lap = 800 meters - **Displacement**: - Since he returns to the starting point after 2 laps, the displacement is 0 meters. ### Diagram for Jermaine: ``` (A)--------------------(B) | | | | | | | | (D)--------------------(C) ``` - **Distance**: 800 meters - **Displacement**: 0 meters --- ### 3. Derrick's Crawl - **Path**: Derrick crawls 4 feet south, then turns east and crawls 6 feet. - **Distance**: - 4 feet (south) + 6 feet (east) = 10 feet - **Displacement**: - To find the displacement, we can use the Pythagorean theorem: - \( d = \sqrt{(4^2 + 6^2)} = \sqrt{16 + 36} = \sqrt{52} \approx 7.21 \) feet - The direction can be found using the tangent function: - \( \tan(\theta) = \frac{opposite}{adjacent} = \frac{4}{6} \) - \( \theta = \tan^{-1}(\frac{4}{6}) \approx 33.69^\circ \) south of east. ### Diagram for Derrick: ``` Starting Point | | (4 feet south) | v (A) | | (6 feet east) --------------------> (B) ``` - **Distance**: 10 feet - **Displacement**: Approximately 7.21 feet at an angle of 33.69° south of east. --- ### Summary of Results: 1. **Amy**: Distance = 5 miles, Displacement = 1 mile north 2. **Jermaine**: Distance = 800 meters, Displacement = 0 meters 3. **Derrick**: Distance = 10 feet, Displacement = approximately 7.21 feet at 33.69° south of east.