lisa walks 10m north, 3m west, 5m north, 12m east and then stops to catch her breath .find her displacement and distance from her original point . then distinguish between displacement and distance
(0,0) to (-3+12,10+5) = (0,0) to (9,15)
distance = 3+12+10+5 = 30
displacement = √(9^2+15^2) = 3√34
To find Lisa's displacement and distance, we need to analyze her movements step-by-step.
1. Lisa walks 10m north: This means she moves 10 meters in the north direction.
2. Lisa walks 3m west: This means she moves 3 meters in the west direction.
3. Lisa walks 5m north: This means she moves 5 meters in the north direction.
4. Lisa walks 12m east: This means she moves 12 meters in the east direction.
To calculate her displacement, we need to find the straight-line distance and direction from her starting point to her final position. We can do this by drawing a vector diagram.
Vector diagram:
Start --- 10m ---→
|
3m
|
5m
|
←--- 12m --- End
From the vector diagram, we can see that the net displacement is the vector that connects her starting point to her final point. By measuring the length and direction of this vector, we can calculate her displacement.
Using the Pythagorean theorem, we can find the displacement as follows:
Displacement = √(10² + 5²) = √(100 + 25) = √125 ≈ 11.18m
To find the distance, we need to calculate the total length of the path traveled. This can be done by adding up all the individual distances traveled.
Distance = 10m + 3m + 5m + 12m = 30m
Now let's distinguish between displacement and distance:
- Displacement: It refers to the straight-line distance from the starting point to the final position, irrespective of the actual path taken. In this case, Lisa's displacement is approximately 11.18m, indicating the shortest distance and direction from her initial point to her final location.
- Distance: It refers to the total path length traveled. In this case, Lisa's distance is 30m, indicating the sum of all the distances covered while walking in different directions.
To summarize, Lisa's displacement is approximately 11.18m towards the northeast, while her total distance traveled is 30m.
To find Lisa's displacement and distance from her original point, we can break down her movements and use the Pythagorean theorem to calculate the distances.
1. Start by drawing a simple diagram to visualize Lisa's movements:
- From the original point, Lisa walks 10 meters north.
- Then, she walks 3 meters west.
- Next, Lisa walks 5 meters north.
- Finally, she walks 12 meters east and stops.
2. Calculate the displacement:
- Displacement refers to the straight-line distance from the starting point to the final position.
- We can calculate the displacement by finding the x and y components of the distance.
- In this case, the horizontal component (x-axis) is the distance Lisa walked east (12 meters) minus the distance she walked west (3 meters). Therefore, the x-component is 12 meters - (-3 meters) = 15 meters.
- The vertical component (y-axis) is the sum of the distances Lisa walked north minus the distance she walked south. So, the y-component is 10 meters + 5 meters = 15 meters.
- Using the Pythagorean theorem, we can find the displacement:
Displacement = √((x^2) + (y^2)) = √((15^2) + (15^2)) = √(225 + 225) = √450 ≈ 21.21 meters.
3. Calculate the distance:
- Distance refers to the total length of the path traveled.
- We can calculate the distance by summing the individual lengths of each segment.
- In this case, Lisa walked 10 meters north, 3 meters west, 5 meters north, and 12 meters east.
- Distance = 10 meters + 3 meters + 5 meters + 12 meters = 30 meters.
So, Lisa's displacement from her original point is approximately 21.21 meters, while the distance she traveled is 30 meters.
The difference between displacement and distance:
- Displacement considers only the starting and ending points, measuring the shortest straight-line distance between them.
- Distance, however, takes into account the total length of the path traveled, regardless of direction.
- Displacement is a vector quantity, as it has both magnitude (distance) and direction.
- Distance is a scalar quantity, as it only has magnitude and does not consider direction.