Vector , which is directed along an x axis, is to be added to vector , which has a magnitude of 5.0 m. The sum is a third vector that is directed along the y axis, with a magnitude that is 5.5 times that of . What is the magnitude of ?

Try filling in u,v,w for the vectors, so we know which vector the sum is a multiple of.

72.7889

To solve this problem, we need to use vector addition and mathematical equations.

Let's start by defining the given information:
- Vector A is directed along the x-axis.
- Vector B has a magnitude of 5.0 m.
- The sum of vectors A and B is a third vector C, directed along the y-axis.
- The magnitude of vector C is 5.5 times that of vector B.

Now, let's assign variables to the magnitudes of vector A and vector C:
- Let's call the magnitude of vector A as A.
- Let's call the magnitude of vector C as C.

We can write the following equations based on the given information:
1) C = 5.5 * B
2) A + B = C

We can substitute the value of B from equation 1 into equation 2:
A + 5.0 = 5.5 * 5.0

Now, we can solve for A:
A + 5.0 = 27.5
A = 27.5 - 5.0
A = 22.5

Therefore, the magnitude of vector A is 22.5 m.

Now, we can find the magnitude of vector C by substituting the value of A and B into equation 2:
22.5 + 5.0 = C
C = 27.5

Therefore, the magnitude of vector C is 27.5 m.