Alex is practicing his dives at a pool. He dives from a diving board that is 15 feet above the surface of the water. His dive takes him 15 feet below the surface of the water. Alex says that the two distances are opposites, so his total dive distance is \( 15+(-15)=0 \) feet. Are the two distances opposites? Is Alex's total dive distance correct? Explain your reasoning.

Alex's reasoning involves a common misunderstanding between **distance** and **displacement**, which are two different concepts in physics. 1. **Are the Two Distances Opposites?** - **Distance** is a **scalar quantity**, meaning it only has magnitude (size) and no direction. When Alex dives, he moves **15 feet downward** from the diving board to the water's surface and then **another 15 feet downward** below the surface. Both movements are in the same direction (downward), so they aren't opposites. - If we were discussing **displacement**, which is a **vector quantity** (having both magnitude and direction), the situation would still not make the two distances opposites. Alex starts 15 feet above the water and ends 15 feet below, resulting in a total **displacement** of **30 feet downward**, not zero. 2. **Is Alex's Total Dive Distance Correct?** - **Distance Calculation:** Since distance is scalar, you simply add the magnitudes without considering direction. Therefore, Alex's total dive distance is: \[ 15 \text{ feet (down to water)} + 15 \text{ feet (below water)} = 30 \text{ feet} \] So, the correct total dive distance is **30 feet**, not **0 feet**. - **Displacement Calculation:** As mentioned, displacement considers direction. Starting 15 feet above and ending 15 feet below the water results in: \[ -15 \text{ feet (from starting point to water)} + (-15 \text{ feet (below water)}) = -30 \text{ feet} \] This indicates a **30-foot downward displacement**. **Conclusion:** - The two distances Alex mentioned are not opposites. - Alex's total dive distance calculation is incorrect because he mistakenly treated the distances as having opposite signs. The correct total dive distance is **30 feet**.