Question

Vector A with arrow, which is directed along an x axis, is to be added to vector B with arrow, which has a magnitude of 5.5 m. The sum is a third vector that is directed along the y axis, with a magnitude that is 6.0 times that of A with arrow. What is the magnitude of A with arrow? (Enter your answer to 4 significant figures.)

Answer 1

Magnitude of vector A = 0.904

Step-by-step explanation:

Vector A , which is directed along an x axis, that is

`\vec{A}=x_A\hat{i}`

Vector B , which has a magnitude of 5.5 m

`\vec{B}=x_B\hat{i}+y_B\hat{j}`

`\sqrt{x_(B)^(2)+y_(B)^(2)}=5.5\\\\x_(B)^(2)+y_(B)^(2)=30.25`

The sum is a third vector that is directed along the y axis, with a magnitude that is 6.0 times that of vector A
`\vec{A}+\vec{B}=6x_A\hat{j}\\\\x_A\hat{i}+x_B\hat{i}+y_B\hat{j}=6x_A\hat{j}`

Comparing we will get

`x_A=-x_B\\\\y_B=6x_A`

Substituting in
`x_(B)^(2)+y_(B)^(2)=30.25`

`\left (-x_(A) \right )^(2)+\left (6x_(A) \right )^(2)=30.25\\\\37x_(A)^2=30.25\\\\x_(A)=0.904`

So we have

`\vec{A}=0.904\hat{i}`

Magnitude of vector A = 0.904