Linear algebra - vectors?

A boat is traveling on a river in a SW direction at 10mph while a passenger is walking from the port to the starboard (from SE side to the NW side of the boat) at 2 mph. Find the velocity %26amp; speed of the passenger with respect to the shore.





--I began by drawing a vector from (0,0) in the 3rd quadrant (b/c its SW) with a length of 10. I have no idea where to go from here.

Linear algebra - vectors?
You are right to add two vectors together and put the tails of both together at the origin.





The first vector for the boat is:


v = (-10i - 10j)/√2





The second vector for the passenger is


w = (-2i + 2j)/√2





v + w = (-12i - 8j)/√2


The magnitude of (v + w) is


√{(12² + 8²)/(√2)²} = √{144 + 64)/2} = √104 = 2√26


This is the passenger's speed.





"Relative to shore" is not well defined because where shore is is not stated. Do you mean speed, or how fast it is moving past the bank of the river? If so, whether the passenger's direction is straight down the river, or whether he is moving partly away from shore and partly down the river cannot be determined.