A lorry travels 10km North's ,4km east,6km south,and 4km west what's the displacement and distance
well, the final location is (0,4) from the starting point, so ...
distance of course is 10+4+6+4 = ?
Well, it looks like the lorry went on a bit of a sightseeing tour! If we break it down, the displacement is the straight-line distance from the starting point to the ending point. In this case, it traveled 10km North and then 6km South, so it canceled out and the displacement is 0km.
However, if you want to calculate the total distance traveled by the lorry, you simply add up all the distances traveled: 10km + 4km + 6km + 4km = 24km. So the total distance traveled is 24km.
Seems like this lorry took the scenic route, but hey, at least they got their steps in!
To find the displacement and distance of the lorry, we need to calculate the total movement in each direction.
1. North: The lorry travels 10km north.
2. East: The lorry travels 4km east.
3. South: The lorry travels 6km south.
4. West: The lorry travels 4km west.
To calculate displacement, we need to find the straight-line distance between the starting point and the ending point. We can use Pythagoras' theorem to calculate this.
Displacement:
The north and south distances cancel each other out, and the east and west distances cancel each other out, so the displacement is given by the formula:
√((east - west)^2 + (north - south)^2)
√((4 - 4)^2 + (10 - 6)^2)
= √(0^2 + 4^2)
= √(0 + 16)
= √16
= 4 km
Therefore, the displacement is 4 km.
Distance:
To calculate the total distance traveled, we need to add up the distances traveled in each direction.
Distance:
North: 10 km
East: 4 km
South: 6 km
West: 4 km
Total distance = 10 km + 4 km + 6 km + 4 km = 24 km
Therefore, the total distance traveled by the lorry is 24 km.
To find the displacement and distance traveled by the lorry, we can visualize its movements on a coordinate plane.
Step 1: Create a coordinate plane with an origin (0,0).
Step 2: Mark the starting point of the lorry on the coordinate plane (0, 0).
Step 3: Identify the direction and distance traveled for each leg of the journey:
1. The lorry travels 10km North, so it moves up along the y-axis by 10 units to the point (0, 10).
2. Then, it travels 4km East, so it moves right along the x-axis by 4 units to the point (4, 10).
3. After that, it travels 6km South, so it moves down along the y-axis by 6 units to the point (4, 4).
4. Finally, it travels 4km West, so it moves left along the x-axis by 4 units to the point (0, 4).
Step 4: Calculate the displacement:
The displacement is the straight-line distance from the starting point to the ending point of the lorry's journey. To find it, we can use the Pythagorean theorem.
Displacement = √(change in x)^2 + (change in y)^2
In this case, the change in x = 0 - 4 = -4 and the change in y = 4 - 10 = -6.
So, Displacement = √((-4)^2 + (-6)^2) = √(16 + 36) = √52 ≈ 7.21 km.
Step 5: Calculate the distance traveled:
To calculate the distance traveled, we sum up the distances traveled along each leg of the journey:
Distance = 10 km + 4 km + 6 km + 4 km = 24 km.
Therefore, the displacement of the lorry is approximately 7.21 km, and the distance traveled is 24 km.