You walk 30 m south and 30 m east. Find the magnitude and direction of the resultant displacement both graphically and algebraically

magnitude of resultant displacement= 42.42

No necessary step shown for problem answer

The question is not clear no step shown

Well, to find the magnitude and direction of the resultant displacement, let's dive into a display of wit and entertainment.

Graphically, we can represent your walk with a coordinate system. Starting at the origin, move 30 m south from (0, 0), and you'll end up at (0, -30). Then, take a glorious stroll 30 m east from there, and you'll reach (30, -30). Now, let's connect the dots and draw a straight line from the starting point to the final point. Voilà! That line represents the resultant displacement.

To determine the magnitude, we focus on the length of the line we just drew. Using the Pythagorean Theorem, we have:

Magnitude = √((Δx)^2 + (Δy)^2)
= √((30)^2 + (-30)^2)
= √(900 + 900)
= √1800
≈ 42.43 m

So, the magnitude of the resultant displacement is approximately 42.43 m.

Now, let's reveal the direction of this marvelous journey! We can find the direction by using trigonometry. Tangents and jokes go hand in hand, don't they? The tangent of an angle is equal to the opposite over the adjacent, so we'll have:

tan(θ) = (Δy) / (Δx)
tan(θ) = (-30) / (30)
= -1

We solve for θ by taking the arctan(-1):

θ ≈ -45°

Thus, the direction of the resultant displacement is approximately 45 degrees south of east.

Algebraically, we can break down your walk into its components. By moving south, you have a displacement of -30 m in the y-direction. And by going east, you walk 30 m in the x-direction. Adding these components algebraically, we have:

Resultant Displacement = √((Δx)^2 + (Δy)^2) ≈ 42.43 m

Direction = atan(Δy / Δx) ≈ -45° (approximately 45 degrees south of east)

There you have it, a humorous explanation of the magnitude and direction of your resultant displacement! Keep laughing and walking, my friend!

The magnitude can be found with the Pythagorean theorem. The direction is southeast. If you want it algebraically, it is tan^-1(1) east of south.

You can do this.

To find the magnitude and direction of the resultant displacement both graphically and algebraically, we can use the Pythagorean theorem and trigonometric functions.

Graphically:
1. Start by drawing a coordinate system with north being the positive y-axis and east being the positive x-axis.
2. Draw an arrow from the origin (0,0) pointing 30 meters south. This arrow should extend downwards.
3. Draw another arrow from the end of the first arrow pointing 30 meters east. This arrow should extend to the right.
4. Connect the starting point of the first arrow with the endpoint of the second arrow. This line represents the resultant displacement.
5. Measure the length of the line connecting the starting point of the first arrow with the endpoint of the second arrow. This length represents the magnitude of the resultant displacement.
6. Use a protractor or any other device to measure the angle between the x-axis and the line connecting the starting point of the first arrow with the endpoint of the second arrow. This angle represents the direction of the resultant displacement.

Algebraically:
1. Start by labeling the initial position (0,0).
2. Walk 30 m south, which can be represented as a displacement of (-30,0).
3. Walk 30 m east, which can be represented as a displacement of (0,30).
4. To find the resultant displacement, add the individual displacements by adding the corresponding components. (-30,0) + (0,30) = (-30,30).
5. Use the Pythagorean theorem to find the magnitude of the resultant displacement. The magnitude (r) is given by r = sqrt(x^2 + y^2), where x and y are the components of the resultant displacement. In this case, r = sqrt((-30)^2 + (30)^2) = sqrt(1800) ≈ 42.43 meters.
6. To find the direction of the resultant displacement, use the inverse tangent function (tan^-1) to find the angle (θ) between the x-axis and the resultant displacement. The angle (θ) is given by θ = tan^-1(y / x), where y and x are the components of the resultant displacement. In this case, θ = tan^-1(30 / -30) ≈ -45 degrees.

Therefore, the magnitude of the resultant displacement is approximately 42.43 meters, and the direction is approximately 45 degrees below the x-axis (south-east).