Need help understanding this problem!

You are given a vector in the xy plane that has a magnitude of 90.0 units and a y component of -40.0 units.

(a) What are the two possibilities for its x component?
I got 80.6 and -80.6.

(b) Assuming the x component is known to be positive, specify the vector which, if you add it to the original one would give a resultant vector that is 90.0 units long and points entirely in the -x direction. What is the magnitude and direction?

Mentor
Think of your original vector in terms of its components. Now think of the resultant vector in terms of its components. (What are those components?)

What do you have to add to the original components to end up with the resultant components? What you have to add are the components of the vector that you need to find. Once you have the components, then figure out its magnitude and direction.

Staff Emeritus
Gold Member
(a) What are the two possibilities for its x component?
I got 80.6 and -80.6.

That's right.

(b) Assuming the x component is known to be positive, specify the vector which, if you add it to the original one would give a resultant vector that is 90.0 units long and points entirely in the -x direction. What is the magnitude and direction?

OK, so your vector can be written as $\vec{v}=80.6\hat{i}-40.0\hat{j}$. What vector would you have to add to that to get a result that has no y-component, and a magnitude of 90? Remember that vectors add componentwise.

what are my original components and my resultant components?

Staff Emeritus
Gold Member
Look at the following equation:

$9+x=14$.

You wouldn't have any problem finding the solution to that, right? Well, this problem is basically the same. Let $\vec{v}=80.6\hat{i}-40.0\hat{j}$, let $\vec{w}=x\hat{i}+y\hat{j}$, and let $\vec{r}$ be their sum. Then set up the vector equation:

$\vec{v}+\vec{w}=\vec{r}$.

You know $\vec{v}$ and you have enough information to determine $\vec{r}$. All you have to do is find $\vec{w}$ by subtraction.

Mentor