A boy walk 5m east, then 4m south and finally 2m west. calculate the magnitude and direction of the resultant displacement.
final location is clearly 3 east, 4 south
draw the diagram, and recall the Pythagorean Theorem.
Then review the tangent function to get the angle.
A student walks 5 m to the east then another 4 m in the same direction. What is the resultant vector?
To calculate the magnitude and direction of the resultant displacement, we can break down the boy's movements into their x and y components.
First, let's consider the x-components:
- The boy walked 5m east, which means he moved 5m in the positive x-direction.
- Then, he walked 2m west, which means he moved 2m in the negative x-direction.
Therefore, the net x-displacement is 5m - 2m = 3m to the east.
Next, let's consider the y-components:
- The boy walked 4m south, which means he moved 4m in the negative y-direction.
Therefore, the net y-displacement is -4m to the south.
To find the resultant displacement, we can use the Pythagorean theorem:
Resultant displacement = √((x-displacement)^2 + (y-displacement)^2)
Resultant displacement = √((3m)^2 + (-4m)^2)
Resultant displacement = √(9m^2 + 16m^2)
Resultant displacement = √(25m^2)
Resultant displacement = 5m
The magnitude of the resultant displacement is 5m.
To find the direction, we can use trigonometry.
tan(θ) = (y-displacement) / (x-displacement)
θ = tan^(-1)((y-displacement) / (x-displacement))
θ = tan^(-1)(-4m / 3m)
θ ≈ -53.13°
The direction of the resultant displacement is approximately 53.13° to the south of east.
To calculate the magnitude and direction of the resultant displacement, we need to find the net displacement vector by adding the individual displacement vectors.
1. Start by drawing a diagram representing the given displacements:
- Draw a line segment of 5m towards the east (right direction).
- Draw a line segment of 4m towards the south (downward direction).
- Draw a line segment of 2m towards the west (left direction).
2. Connect the starting point of the first displacement vector (east) to the endpoint of the last displacement vector (west). This line will represent the resultant displacement vector.
3. Measure the length of the resultant displacement vector using a ruler or scale.
4. Use the Pythagorean theorem to find the magnitude of the resultant displacement:
Magnitude = sqrt((east-west)^2 + (north-south)^2)
In this case:
Magnitude = sqrt((5-2)^2 + (0-4)^2)
= sqrt(3^2 + (-4)^2)
= sqrt(9 + 16)
= sqrt(25)
= 5
So, the magnitude of the resultant displacement is 5m.
5. Determine the direction of the resultant displacement using trigonometry. You can calculate the angle between the resultant displacement vector and the east axis using the inverse tangent function:
Direction = atan((north-south) / (east-west))
In this case:
Direction = atan((0-4) / (5-2))
= atan(-4/3)
≈ -53.1°
The negative sign indicates that the direction is to the south from the east axis.
Therefore, the magnitude of the resultant displacement is 5m, and the direction is approximately 53.1° south of east.