Answer:
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:
[tex]|B|=\sqrt{B_x^2+B_y^2}=\sqrt{(-A_x)^2+(3A_x)^2}=\sqrt{A_x^2+9A_x^2}=\sqrt{10A_x^2}=\sqrt{10}A_x[/tex]
And we know that this must be 9m
[tex]\sqrt{10}A_x=9m[/tex]
Which means
[tex]A_x=\frac{9m}{\sqrt{10}}=2.84604989415m[/tex]
But we also know that the magnitude of A is Ax, so (with 4 significant figures):
[tex]|A|=\frac{9m}{\sqrt{10}}=2.846m[/tex]
