How Do You Calculate Relative Velocity and Minimum Distance Between Two Boats?

[BryceA]

Okay here goes!

A boat "A" travels due north at a velocity of 18km/h , and a boat "B" travels south-east at 15km/h.

a) Calculate the velocity of "A" relative to "B".

b) If "B" is initially 30km north of "A", calculate the shortest distance between the two boats during the motion.
Right, so I as able to work out a) by simply drawing my vector diagram and then using the cosine rule to calculate the Vab (velocity of A relative to B) to be: 30.51km/h

Now what I can't figure out is how to place this new information given in b), I think its the phrasing that's tricking me, maybe.

PLEASE HELP! I just have to know how to do this one!

 

[voko]

30.51 km/h is not velocity. It is speed. Velocity has a direction - what is it?

Assuming you do have velocity of A relative to B, you can treat B as if it were stationary. So it is a point. The trajectory of A is then given by a straight line. Find the distance between the point and the line.

 

[BryceA]

That makes sense! Let me give it a try and see what I get! Thank you voko :)

 

[BryceA]

Okay now this is what is strange... When I do it the way I would if I were working with speed, I'm getting an answer completely different from what the model answer of the textbook is. The textbook reckons it should be 10.428km but I cannot understand how they would get such a value. If they want me to calculate the SHORTEST DISTANCE between them, then it means I must also have a time variable... Where in the world does this come from now?

 

[voko]

In geometry, the distance between a point and a straight line is the shortest distance between them, by definition.

You do not have to involve time in this (even though you could). You just need to figure out how the point and the line are situated, and use a bit of geometry.

 

[azizlwl]

As Mr Voko said you have to understand what relative speed means. Find relative velocity of B to A. From north B is traveling south-east. The shortest is the perpendicular line from line B to point A

 

[BryceA]

Now I see what you guys are trying to say. After I drew a new vector diagram, it kinda came together! I think its my misunderstanding of the concept of relative velocity that needs work. Thank you so much guys! Now I can breathe...