Question

A vector B , with a magnitude of 8.0 m, is added to a vector A , which lies along an x axis. The sum of these two vectors is a third vector that lies along the y axis and has a magnitude that is twice the magnitude of A . What is the magnitude of A?

Answer 1

the magnitude of A is 3.577

Step-by-step explanation:

According to the question it is given that there is a magnitude of 8.0 m that added to the vector A that lies on x axis also the sum of two vectors would be third vector by considering the y axis and the magnitude is the twice of the magnitude B

The computation of the magnitude of A is shown below:

`A \hat{i} + B = 2A \hat{j}\\\\A \hat{i} + 8 = 2A \hat{j}\\\\8 = 2A \hat{j} - A \hat{i}\\\\\mid8\mid = \sqrt{(2A \hat{j})^2 + (- A \hat{i})^2} \\\\8 = √(5A) \\\\A = (8)/(√(5) )`

A = 3.577

Hence, the magnitude of A is 3.577