**Problem Statement:** A bicycle travels 6.00 km due east in 0.100 h, then 9.20 km at 15.0° east of north in 0.550 h, and finally another 6.00 km due east in 0.100 h to reach its destination. The time lost in turning is negligible. Assume that east is in the +x-direction and north is in the +y-direction. **Question:** What is the magnitude of the average velocity for the entire trip? **(Answer Box: _______ km/h)** --- **Explanation (for educational purposes):** To calculate the magnitude of the average velocity, one must consider: 1. **Displacement:** It is a vector quantity. Sum up the displacement vectors from each leg of the trip: - First leg: 6.00 km east. - Second leg: 9.20 km at 15.0° east of north. Break this into components: - \( x \)-component = \( 9.20 \cdot \cos(15.0°) \) - \( y \)-component = \( 9.20 \cdot \sin(15.0°) \) - Third leg: 6.00 km east. - Total \( x \)-component = \( 6.00 + 9.20 \cdot \cos(15.0°) + 6.00 \) - Total \( y \)-component = \( 9.20 \cdot \sin(15.0°) \) 2. **Total Time:** Add the time for each segment: - \( 0.100 \, \text{h} + 0.550 \, \text{h} + 0.100 \, \text{h} \) 3. **Average Velocity:** - Calculate the magnitude using the components: - \( \text{Magnitude} = \sqrt{(\text{Total } x \text{-component})^2 + (\text{Total } y \text{-component})^2} \) - Divide the magnitude by total time to find average velocity. Ensure you substitute the correct values and solve step by step to find the final average velocity. **Physics Problem: Average Velocity Calculation** **Required Information:** A bicycle travels 6.00 km due east in 0.100 h, then 9.20 km at 15.0° east of north in 0.550 h, and finally another 6.00 km due east in 0.100 h to reach its destination. The time lost in turning is negligible. Assume that east is in the +x-direction and north is in the +y-direction. **Question:** What is the direction of the average velocity for the entire trip? Enter the answer as an angle in degrees north of east. **Answer Input Box:** - _______ ° north of east --- **Explanation:** The problem involves calculating the average velocity of a bicycle trip with three segments. The first and last segments are due east, while the middle segment is angled at 15.0° east of north. To solve, decompose each segment into its x (east) and y (north) components, sum these components, and then calculate the direction of the resultant vector.