A boy moves 400m towards north 300m towards west and again 400m towards south calculate displacement of the boy from initial position
To calculate the displacement of the boy from the initial position, we need to find the net distance and direction between the initial and final positions.
Let's break down the movements of the boy into vectors:
1. Moving 400m towards north: This can be represented as a vector in the positive y-axis direction with a magnitude of 400m.
2. Moving 300m towards west: This can be represented as a vector in the negative x-axis direction with a magnitude of 300m.
3. Moving 400m towards south: This can be represented as a vector in the negative y-axis direction with a magnitude of 400m.
To calculate the net displacement, we need to add these vectors together:
Net displacement = (400m North) + (-300m West) + (-400m South)
To simplify the calculation, we can convert the direction to a common coordinate system. Let's consider North as positive y-axis and East as positive x-axis.
Net displacement = (400m, 0m) + (-300m, 0m) + (0m, -400m)
Adding the components:
x-axis component: 0m - 300m + 0m = -300m
y-axis component: 400m + 0m - 400m = 0m
Therefore, the net displacement of the boy from the initial position is (-300m, 0m). This means the boy has moved 300m towards the west from the starting position.
To calculate the displacement of the boy from his initial position, we can use vector addition.
Step 1: Assign the directions as positive and negative values. Let's assume north as positive and south as negative, while west as negative and east as positive.
Step 2: Break down the given movements into x and y components.
The boy moves 400m towards the north, so his movement in the y-axis is +400m.
The boy moves 300m towards the west, so his movement in the x-axis is -300m.
The boy moves 400m towards the south, so his movement in the y-axis is -400m.
Step 3: Calculate the displacements in the x and y directions separately.
In the x-axis, the displacement is the sum of all x components:
Displacement in x = -300m
In the y-axis, the displacement is the sum of all y components:
Displacement in y = +400m - 400m = 0
Step 4: Use the Pythagorean theorem to find the magnitude of the displacement.
Displacement = √((Displacement in x)^2 + (Displacement in y)^2)
Displacement = √((-300m)^2 + 0^2)
Displacement = √(90000m^2)
Displacement = 300m
Therefore, the displacement of the boy from his initial position is 300 meters.
300 m. (Towards West ).
north = 400 - 400 = 0
west = 300
d = sqrt (0^2 + 300^2)
= 300
I have a hunch you have a typo.