A person walks from point A to point B as shown in the figure below. What is the person's displacement relative to A?
What is the magnitude?
What is the direction ° (counterclockwise from the +x-axis)?
27m at 72 degrees
To determine the person's displacement relative to point A, we need to find the straight-line distance between point A and point B.
To find the magnitude of the displacement, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). In this case, the displacement is the hypotenuse of a right triangle:
Displacement = √(Δx^2 + Δy^2)
To find the direction in degrees counterclockwise from the +x-axis, we can use trigonometry. We can find the angle θ using the equation:
θ = tan^(-1)(Δy / Δx)
Now, let's calculate the displacement, magnitude, and direction relative to point A based on the information given in the figure.
To determine the person's displacement relative to point A, we need to find the straight-line distance and direction from A to B.
The figure provided is necessary to determine the direction, but it is not present in the text. Please describe the figure or provide more information about the relative positions of points A and B, and any possible paths between them.
Once we have this information, I can guide you through the process of calculating the displacement, magnitude, and direction.
OK, I found the figure at
http://www.webassign.net/wb/3-30.gif
All you have to do is use a little trig and add up the vertical and horizontal displacements.
Four vectors are being added. In the +y direction, the change in position is
Y = 20 sin 30 + 30 - 20 sin 45
= 25.86 m
You do the +x displacement, which is
X = 20 cos30 -40 + 20 cos 45, which is a negative number.
Use the Pythagorean theorem for the magnitude of the displacement.
The direction angle is in the second quadrant and the tangent of the angle from the +X axis is Y/X