Questions: 9. A spring-loaded toy is launched straight upward from the surface of a table. In Case 1, the toy is caught at the instant that it reaches its highest point and held at rest. In Case 2, the toy is allowed to rise, then fall back to the table. In which case is the magnitude of the average velocity of the toy's free-fall motion the greatest? (A) Case 1, because the toy travels for less time (B) Case 1, because the toy has a greater displacement (C) Case 2, because the toy travels a greater distance (D) Case 2, because the toy travels for a longer time

Solution Steps

We need to determine in which case the magnitude of the average velocity of the toy's free-fall motion is the greatest. The average velocity is defined as the total displacement divided by the total time taken.

In Case 1, the toy is caught at its highest point. The displacement is from the table to the highest point. Since it is caught at the highest point, the time of free-fall motion is zero after reaching the highest point.

In Case 2, the toy rises to its highest point and then falls back to the table. The displacement for the entire motion is zero because it starts and ends at the same point (the table). However, the time taken includes both the ascent and descent.

• Case 1: The average velocity is calculated as the displacement (from the table to the highest point) divided by the time taken to reach the highest point.
• Case 2: The average velocity is zero because the displacement is zero (it returns to the starting point).

Final Answer