Grade 12 PhysicProblem?
A boat travels directly north across a river at a velocity of 1.0m/s. if the river flows at a velocity of 0.5m/s east, in what direction is the boat headed relative to the river? (Note: Resultant is perpendicular to the river current. The 1.0m/s is resultant).
Comments
I will first repose your question, assuming you are learning about vector addition in class right now.
QUESTION:
Suppose a frame of reference fixed to the bank. y is North, x is East. In this frame of reference, the velocity vector of your boat V is
v = (0 1) m/s
(In plain English, boat is traveling North at 1 m/s)
Now consider a frame moving with the water in the river, axes coincident with those of the fixed frame described above. The origin of the moving frame is traveling with velocity w = (0.5 0) m/s when viewed from the fixed frame.
(In plain English, water is moving East at 0.5 m/s)
The question is, what is the velocity vector v' of the boat as viewed from the frame moving with the water?
(In plain English, if you were drifting East in the water, what direction do you see the boat moving?)
ANSWER:
If you are looking for a Newtonian answer, Galilean relativity states that
v' = v - w
Hence
v' = (-0.5 1) m/s
If by "direction", you mean angle relative to the y/y' axis, the answer is
arctan(0.5/1) = arctan(0.5) ~ 26.5 degrees West of North.