To analyze the motion of the ball thrown vertically upwards from position P, we can break down the question into two main components: net displacement and total distance traveled.
### Net Displacement
1. Net Displacement Definition: Displacement is a vector quantity that refers to the change in position of an object. It is calculated as the straight-line distance from the initial position to the final position, along with a specified direction.
2. Initial and Final Positions: In this scenario, the ball starts at position P, rises to the highest point Q, and eventually returns back to position P. Since the ball returns to its starting point, the initial and final positions are the same.
3. Calculation: The change in position (displacement) is zero because the ball ends up exactly where it started.
[tex]\[
\text{Net Displacement} = 0 \text{ units}
\][/tex]
### Total Distance Traveled
1. Distance Definition: Distance is a scalar quantity that refers to the total path length traveled by an object irrespective of direction. It's always positive or zero, never negative.
2. Path of the Ball: The ball moves from position P to the highest point Q and then back from Q to P. The movement consists of two parts:
- The distance from P to Q (upwards).
- The distance from Q to P (downwards).
3. Calculation:
- Let the height of the highest point Q from position P be H.
- Therefore, the ball travels a distance H upwards.
- It then travels the same distance H downwards to return to position P.
- The total distance traveled is the sum of these two distances:
[tex]\[
\text{Total Distance} = H (\text{up}) + H (\text{down}) = 2H
\][/tex]
4. Example: If we assume the height \(H\) the ball reaches from position P is 10 units, then:
[tex]\[
\text{Total Distance} = 2 \times 10 = 20 \text{ units}
\][/tex]
### Conclusion
- Net Displacement: The net displacement of the ball is \(0\) units.
- Total Distance Traveled: The total distance traveled by the ball is \(20\) units.
These are the results of the ball's motion when thrown vertically upwards from position P, rising to the highest point Q, and then returning back to position P.
