Hi all,

Question

I have been given component x- and y- for F1=(8.0*10^7N,7.0*10^7N)
F2=(4.0*10^7N,-2.0*10^7N) for an object.

Which following my textbooks have found the following vector components:
F1+F2=(1.2*10^8N,5.0*10^7N)

Now I want to find the distance from earth that this object has the same magnitude force as above.

So I was thinking of using F=Gm1+m2/d^2

but in order to do this I want to rearrange the equation to solve for d^2... however im unsure how to work with component vectors in this form i.e should I add the x and y components together to end up with 1.7*10^8N? and then set that as F?

Any pointers would be great!
Thanks

Answer 1

|F1+F2| = √((1.2*10^8)^2+(5.0*10^7)^2)
= 10^8 √(1.2^2 + 0.5^2)
= 1.3*10^8 N

So, you want d such that

GMm/d^2 = 1.3*10^8

Now just plug in G and the masses and crank out d.

Answer 2

Thanks Steve I assumed as much but just wanted to be sure.