if a girl walks 30m northwards from point A-B and then 40m eastwards to point C.What is her total displacement and distance?
Disp. = 30i + 40 = 50m[36.9o].
dist. = 30 + 40 = 70 m.
To find the girl's total displacement, we can use vector addition.
First, let's draw a diagram to visualize the situation. Place point A at the origin (0,0) and point B north of A. Then, move 30 meters northwards to point B. Next, move 40 meters eastwards to point C.
Now, we need to find the coordinates of points B and C.
Point B is 30 meters north of point A, so the coordinates of point B would be (0, 30).
Point C is 40 meters east of point B. Since we moved to the east, the x-coordinate increases by 40, while the y-coordinate remains the same. So the coordinates of point C would be (40, 30).
Using the coordinates of points A and C, we can calculate the girl's displacement. Displacement is the straight-line distance between the starting point (A) and the ending point (C). We can use the distance formula to find it:
Displacement = √((xC - xA)^2 + (yC - yA)^2)
Substituting the coordinates, we get:
Displacement = √((40 - 0)^2 + (30 - 0)^2)
Displacement = √(40^2 + 30^2)
Displacement = √(1600 + 900)
Displacement = √(2500)
Displacement = 50 meters (rounded to the nearest meter)
So, the girl's total displacement is 50 meters.
To find the girl's total distance traveled, we add up the individual distances traveled along each leg of the journey.
The distance traveled from A to B is 30 meters, and the distance traveled from B to C is 40 meters. Adding these distances together, we have:
Total distance = 30 + 40
Total distance = 70 meters
Therefore, the girl's total distance traveled is 70 meters.