24. 0/3 points All Submissions Notes Question: Walker2 3.P.015.
Question part Points Submissions 1 2 3
0/1 0/1 0/1
0/7 3/7 2/7
Total 0/3 A vector A has a magnitude of 49.0 m and points in a direction 20.0° below the x axis. A second vector, B, has a magnitude of 70.0 m and points in a direction 41.0° above the x axis.
Find the magnitude and direction of the vector D.
I do not see how the vector D is defined. I have to assume that vector D is the sum of vectors A and B.
To find the resultant (sum) of vectors, you would sum the x- and y-components by resolving the vectors in the x-direction (Pcos(θ)) and y-direction (Psin(θ)).
The magnitude of the resultant is
sqrt(SumX²+SumY²)
and the direction is obtained by
atan(SumY/SumX).
Pay attention to the quadrant of the angle by observing the signs of SumX and SumY.
To find the magnitude and direction of the vector D, we need to combine the vectors A and B using vector addition.
Step 1: Draw the vectors A and B on a coordinate plane.
- Draw a vector A with a length of 49.0 m pointing 20.0° below the x-axis.
- Draw a vector B with a length of 70.0 m pointing 41.0° above the x-axis.
Step 2: Break down the vectors A and B into their x and y components.
- For vector A:
- The x-component (Ax) can be found using the formula `Ax = A * cos(angle)`, where angle is the angle below the x-axis.
- The y-component (Ay) can be found using the formula `Ay = A * sin(angle)`.
- For vector B:
- The x-component (Bx) can be found using the formula `Bx = B * cos(angle)`, where angle is the angle above the x-axis.
- The y-component (By) can be found using the formula `By = B * sin(angle)`.
Step 3: Calculate the x and y components of the vector D by adding the corresponding components of A and B.
- Dx = Ax + Bx
- Dy = Ay + By
Step 4: Find the magnitude of the vector D using the Pythagorean theorem.
- Magnitude D = sqrt(Dx^2 + Dy^2)
Step 5: Find the direction of the vector D using the inverse tangent function.
- Direction D = atan(Dy / Dx)
Now, let's plug in the values and solve for the magnitude and direction.
Ax = 49.0 m * cos(20°) = 46.63 m (rounded)
Ay = 49.0 m * sin(20°) = -16.77 m (rounded)
Bx = 70.0 m * cos(41°) = 53.41 m (rounded)
By = 70.0 m * sin(41°) = 46.41 m (rounded)
Dx = Ax + Bx ≈ 46.63 m + 53.41 m
Dy = Ay + By ≈ -16.77 m + 46.41 m
Magnitude D = sqrt(Dx^2 + Dy^2)
Direction D = atan(Dy / Dx)
Now, calculate the values for the magnitude and direction of the vector D.