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

Answer:

Magnitude of vector A = 0.904

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