Question

You are given a vector in the xy plane that has a magnitude of 94.0 units and a y component of -44.0 units.

A. What are the two possibilities for its component?

For this part I got x = 83.1 and -83.1

B. Assuming the x component is known to be positive, specify the vector V which, if you add it to the original one, would give a resultant vector that is 61.0 units long and points entirely in the -x direction.

This is where I'm stuck. I tried working it out like this:

x^2 + y^2 = r^2
x^2 + (44)^2 = (61)^2
x = 42.25

But it's wrong. Though, I'm sure that the y component for this second vector should be positive 44 to cancel out with the -44 from the first vector to get the third one.

Please, help?

Answer 1

You need to add a vector with y component of +44 (to cancel the -44) and an x component of -(83.1 +61) = -144.1.

The equation you are using is not the right one. The vector you add is not the vector you end up with. For the x component, you start with 83.1 and end up with -61.