a person moves 30m north, then 20m east and then 30(square root of two)m south west . His displacement from the original position is ?.
Draw 3 vectors from the origin:
20m @ 0 Deg.(East).
30m @ 90 Deg.(North).
30*sqrt2 @ (270-45)Deg.(Southwest).
X = Hor. = 20 + 30*sqrt2*cos225 = -10m.
Y = Ver. = 30 + 30*sqrt2*sin225 = 0.
D = sqrt(X^2+Y^2)
D = sqrt(100+0) = 10 m.
NOTE: sqrt = Square root.
To find the displacement from the original position, we need to calculate the net movement of the person in terms of both direction and magnitude.
First, the person moves 30 meters north. This means the person's movement can be represented as +30m in the north direction.
Then, the person moves 20 meters east. This can be represented as +20m in the east direction.
Lastly, the person moves 30√2 meters southwest. To simplify this, we can split the southwest movement into its components. Since southwest means going diagonally towards the direction halfway between south and west, we can split it into an equal movement of 30√2/2 or 15√2 meters each in the south and west directions. Thus, the person's movement can be represented as -15√2m in the south direction and -15√2m in the west direction.
To find the total displacement, we need to add up the movements in each direction. Let's calculate:
North: +30m
East: +20m
South: -15√2m
West: -15√2m
Total displacement in the north direction: +30m
Total displacement in the east direction: +20m
Total displacement in the south direction: -15√2m
Total displacement in the west direction: -15√2m
Now, to find the overall displacement, we can add up the displacements in each direction:
Overall displacement in the north direction: +30m + (-15√2m)
Overall displacement in the east direction: +20m + (-15√2m)
We can't directly add meters with meters times the square root of 2, so we can't simplify this further without a calculator.
Therefore, the final displacement from the original position is:
Overall displacement = (30m + (-15√2m)) in the north direction + (20m + (-15√2m)) in the east direction
We can write this in a simplified form, but we cannot calculate the exact numerical value without knowing the value of √2.