Question

A ball is rolled uphill a distance of 5 meters before it slows, stops, and begins to roll back. The ball rolls downhill 9 meters before coming to rest against a tree.

What is the amount of displacement of the ball?


14 meters

9 meters

4 meters

45 meters

Answer 1

Displacement is defined as the straight-line distance from the initial position to the final position, taking into account the direction.

1. The ball is rolled uphill 5 meters.
2. Then it rolls back downhill 9 meters.

To find the displacement, we can calculate the starting position as 0 meters (the position at the top of the hill after rolling up) and then evaluate the final position after rolling back downhill.

When it rolls uphill 5 meters, it reaches a position of +5 meters. Upon rolling back downhill 9 meters:

\[
+5 \text{ meters} - 9 \text{ meters} = -4 \text{ meters}
\]

The final position is -4 meters, meaning it is 4 meters past the original starting point in the opposite direction.

The total displacement from the initial position (0 meters) to the final position (-4 meters) is:

\[
0 - (-4) = -4 \text{ meters}
\]

In terms of magnitude, the displacement is 4 meters in the direction opposite to the initial roll.

Thus, the answer is **4 meters**.