Real World Vector and Trig Issue

[En1gma]

A ship is travelling in seas at a speed relative to the surrounding sea of 25kmh−1 with a bearing of 140◦. It is on course to to make to a port. Unfortunately, during the night a strong current arises, of 5kmh−1 in the direction from south-west to north-east. If the ship was 150km from the port when a current arose and heading at a right angle to a beach that is approximately a straight line, by how much will the ship miss the port because of the current?

I've been thinking about this for quite a while. I haven't had much luck finding a solution. I have been given the current velocity, but I'm unsure as to the significance of the right angle in the question. I'm attempting to visualise the problem without much luck. What I've thought of is adding the current vector to the distance vector of 150km and using it's x value as the distance the ship missed the port by once the current effects it (this would be taking into account the right angle in the problem). Am I on the correct track at all here? Any help would be much appreciated. I can't get this out of my head!

I have calculated the original velocity of the ship and the current in component form, as well as the resultant velocity of the two (in component, as well as magnitude and bearing).

 

[Deleted member 4993]

I've been thinking about this for quite a while. I haven't had much luck finding a solution. I have been given the current velocity, but I'm unsure as to the significance of the right angle in the question. I'm attempting to visualise the problem without much luck. What I've thought of is adding the current vector to the distance vector of 150km and using it's x value as the distance the ship missed the port by once the current effects it (this would be taking into account the right angle in the problem). Am I on the correct track at all here? Any help would be much appreciated. I can't get this out of my head!

Distance is NOT a vector.

I suspect that you have not posted the complete problem.

Please post the COMPLETE problem.

 

[En1gma]

I've edited the original question with more information.

 

[Deleted member 4993]

I've been thinking about this for quite a while. I haven't had much luck finding a solution. I have been given the current velocity, but I'm unsure as to the significance of the right angle in the question. I'm attempting to visualise the problem without much luck. What I've thought of is adding the current vector to the distance vector of 150km and using it's x value as the distance the ship missed the port by once the current effects it (this would be taking into account the right angle in the problem). Am I on the correct track at all here? Any help would be much appreciated. I can't get this out of my head!

I have calculated the original velocity of the ship and the current in component form, as well as the resultant velocity of the two (in component, as well as magnitude and bearing).

You will need to add the VELOCITY of the ship and the VELOCITY of the current - vectorially.

 

[En1gma]

You will need to add the VELOCITY of the ship and the VELOCITY of the current - vectorially.

I had already calculated this. But what I'm mainly confused about is how to calculate how much it misses the port by. What is the significance of the right angle and the 300km distance? Thanks!

 

[HallsofIvy]

Adding those two vectors gives the line that the boat moves along. The shortest distance between a point and such a line is measured along a line, through the given point perpendicular to the given line.