Question

Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectively. If these two vectors are added together, the magnitude of the sum

Answer 1

To find the magnitude of the sum of two displacement vectors, break down each vector into its components, add the x-components and y-components separately, and then use the Pythagorean theorem to find the magnitude of the sum.

Step-by-step explanation:

To find the magnitude of the sum of two displacement vectors, you can use the graphical method or the component method. In this case, we will use the component method. Let's say vector A has a magnitude of 5.0 m and vector B has a magnitude of 7.0 m. We can break down vector A into its components: Ax = 5.0 m and Ay = 0 m since it is pointing east. Similarly, vector B can be broken down into its components: Bx = 0 m and By = -7.0 m since it is pointing south.

To find the components of the sum of the two vectors, we add the x-components and y-components separately. So, the x-component of the sum, Sx = Ax + Bx = 5.0 m + 0 m = 5.0 m. And the y-component of the sum, Sy = Ay + By = 0 m + (-7.0 m) = -7.0 m.

Now, we can use the Pythagorean theorem to find the magnitude of the sum: |S| = sqrt(Sx^2 + Sy^2) = sqrt((5.0 m)^2 + (-7.0 m)^2) = sqrt(25.0 m^2 + 49.0 m^2) = sqrt(74.0 m^2) ≈ 8.6 m.

Answer 2

8.6m

Step-by-step explanation:

Step one:

given data

we are given two displacement vectors of magnitudes 5 and 7m

Let us assume they are in the same direction and they are acting perpendicular to each other.

Step two:

The magnitude of the vector sum is the resultant vector

which is found by

R^2=5^2+7^2

R^2= 25+49

R^2=74

R=√74

R=8.6m