How do I find the correct magnitude using vectors and magnitudes?

[Oblivion77]

Hey guys, I am posting this question because I don't know what it is asking of me. Here it is:

Any tips or help would be nice. Thanks.

 

[michalll]

You probably have to detemine the i vector component of the astronaut's speed to hit the airlock.

 

[Oblivion77]

How do I go about doing that? The pictures confuses me.

 

[michalll]

Sorry I got it wrong, you have to determine the part of the velocity verctor that is parraler to the verctor pointing from astronaut to the airlock. Which is $$|\overline{v}| cos \varphi$$. Using $$|\overline{v}||\overline{u}|cos \varphi = |\overline{v}\cdot\overline{u}|$$ you should get it.

 

[Oblivion77]

OK thanks that makes sense. So would I Subtract Ra from Rg to get a vector and use the dot product with the velocity vector?

 

[michalll]

Right.

 

[Oblivion77]

What am I doing wrong here. Here is the steps I was doing.
1. U = Rg - Ra = 72.2i + 100j + 154k

2. U . V (dot product) = -880

3. magnitude of V = 4.798. magnitude of U= 197.3

4. -880/ (197.4 x 4.798) = -0.9296 = 158.374 degrees (using cos)

5. magnitude of of V x Cos(158.374) = -4.46 <------ not correct

Please help!