1. The problem is to match each height graph (A, B, C) with its corresponding velocity graph (P, Q, R), knowing that velocity is the derivative of height. 2. Recall that the derivative of a function gives the slope of the function at each point. So, the velocity graph shows the slope of the height graph. 3. Analyze Height graph A: It starts at zero, rises steeply to a peak, then decreases sharply. This means the slope (velocity) starts positive, reaches zero at the peak, then becomes negative sharply. 4. Velocity graph R starts near zero, rises to a positive peak, then falls sharply below zero. This matches the slope behavior of Height graph A. 5. Analyze Height graph B: It starts at zero, rises gradually to a peak, then decreases abruptly. The slope starts positive, decreases to zero at the peak, then becomes negative abruptly. 6. Velocity graph P starts positive, decreases, crosses zero, goes negative, then stabilizes near zero. This matches the slope behavior of Height graph B. 7. Analyze Height graph C: It starts at zero and increases smoothly, approaching a horizontal asymptote. The slope is positive and decreases asymptotically toward zero without crossing zero. 8. Velocity graph Q starts positive and decreases asymptotically toward zero without crossing the axis. This matches the slope behavior of Height graph C. 9. Therefore, the matches are: - Height A with Velocity R - Height B with Velocity P - Height C with Velocity Q Final answer: - C matches Q - B matches P - A matches R