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 9.0 m. the sum is a third vector that is directed along the y axis, with a magnitude that is 3.0 times that of a with arrow. what is the magnitude of a with arrow? (enter your answer to 4 significant figures.)

2.846m

Explanation:

We need to separate each component, and we will write them in the form (x,y), so each vector is:

A: (Ax, Ay)

B: (Bx,By)

A+B: (Ax+Bx, Ay+By).

We know that A is along the x axis, so Ay=0.

We know that A+B is in the y axis, so Ax+Bx=0, which means Bx=-Ax.

For now then we have:

A: (Ax,0)

B: (-Ax,By)

A+B: (0,By)

Clearly the magnitude of A is Ax, and the magnitude of A+B is By (we could use Pythagoras but since it is not necessary we will reserve that for B), and since we know that A+B magnitude is 3 times that of A we know that By=3Ax. This means then that:

B: (-Ax,3Ax).

We now calculate the magnitude of B using Pythagoras:

And we know that this must be 9m

Which means

But we also know that the magnitude of A is Ax, so (with 4 significant figures):

report!

explanation:

physics means: "the branch of science concerned with the nature and properties of matter and energy. the subject matter of physics, distinguished from that of chemistry and biology, includes mechanics, heat, light and other radiation, sound, electricity, magnetism, and the structure of atoms."