# Vector and coordination

#### Renato

##### New member
Hello,

I am so desperate that I have decided to post my question here. I've been searching on Google and Youtbe but nothing really helped me.

Here is my question.

One ship (A) Bobby is sailing calm seas at a speed (relative to the surrounding sea) of 30km on bearing of 40(degree) and another ship (B) Tom sailing calm seas at a speed (relative to the surrounding sea) of 35km on a bearing of 130 (degree). Ship (B) cross the path of ship (A) at right angle.

Question: express in component form velocity for ship (A) Bobby and velocity for ship (B) Tom, both relative to the sea, give the numerical values in km to two decimal points.

Can someone explain give an clear guidance of how to solve this question ?

I supposed to draw a diagram as well (triangle).

I will really appreciate it.

kind regards

#### HallsofIvy

##### Elite Member
"Component form" for a vector means separating the "x" and "y" components. (Of course, in a problem like this, where we are not given a coordinate system, you have to decide which direction is the "positive x-axis" and which the "positive y-axis". The usual convention is that "positive x-axis" is East and "positive y-axis" is North.) A vector of length r in direction $$\displaystyle \theta$$ from North has components $$\displaystyle (r cos(\theta), r sin(\theta))$$. A velocity vector "30km on bearing of 40(degree)" (actually that should be "30 km per hour") is $$\displaystyle (30 cos(40), 30 sin(40))= (23, 29)$$ (rounded to two significant figures).