Answer :
Certainly! Let's consider a body that is thrown vertically upward and reaches a maximum height [tex]\( h \)[/tex] before coming back down to its starting position. We need to determine the total distance traveled by the body and its displacement.
### Part (a): Total Distance Traveled by the Body
1. Upward Journey:
- The body starts from the ground and moves upward to reach the maximum height [tex]\( h \)[/tex].
2. Downward Journey:
- From the maximum height [tex]\( h \)[/tex], the body then returns back to the starting position.
The total distance traveled is the sum of the distance covered during the upward and the downward journeys.
- Distance covered upward = [tex]\( h \)[/tex]
- Distance covered downward = [tex]\( h \)[/tex]
Thus, the total distance traveled by the body is:
[tex]\[ \text{Total Distance} = h \; \text{(upward)} + h \; \text{(downward)} = 2h \][/tex]
### Part (b): Displacement of the Body
1. Initial Position:
- The body starts from the initial position, which we can denote as the origin [tex]\( (0) \)[/tex].
2. Final Position:
- After traveling upward to height [tex]\( h \)[/tex] and then coming back down, the body returns to the initial position.
Displacement is defined as the change in position from the initial point to the final point. Since the body returns to its starting point, the change in position is zero.
Thus, the displacement of the body is:
[tex]\[ \text{Displacement} = \text{Final Position} - \text{Initial Position} = 0 - 0 = 0 \][/tex]
### Summary
- Total Distance Traveled: [tex]\( 20 \)[/tex]
- Displacement: [tex]\( 0 \)[/tex]
So, the body travels a total distance of 20 units and its displacement is 0 units.
### Part (a): Total Distance Traveled by the Body
1. Upward Journey:
- The body starts from the ground and moves upward to reach the maximum height [tex]\( h \)[/tex].
2. Downward Journey:
- From the maximum height [tex]\( h \)[/tex], the body then returns back to the starting position.
The total distance traveled is the sum of the distance covered during the upward and the downward journeys.
- Distance covered upward = [tex]\( h \)[/tex]
- Distance covered downward = [tex]\( h \)[/tex]
Thus, the total distance traveled by the body is:
[tex]\[ \text{Total Distance} = h \; \text{(upward)} + h \; \text{(downward)} = 2h \][/tex]
### Part (b): Displacement of the Body
1. Initial Position:
- The body starts from the initial position, which we can denote as the origin [tex]\( (0) \)[/tex].
2. Final Position:
- After traveling upward to height [tex]\( h \)[/tex] and then coming back down, the body returns to the initial position.
Displacement is defined as the change in position from the initial point to the final point. Since the body returns to its starting point, the change in position is zero.
Thus, the displacement of the body is:
[tex]\[ \text{Displacement} = \text{Final Position} - \text{Initial Position} = 0 - 0 = 0 \][/tex]
### Summary
- Total Distance Traveled: [tex]\( 20 \)[/tex]
- Displacement: [tex]\( 0 \)[/tex]
So, the body travels a total distance of 20 units and its displacement is 0 units.
