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):

explanation:

an enlarged virtual image is the answer

jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.