A passenger walks from one side of a ferry to the other as it approaches a dock.Passenger's velocity is 1.60 due north relative to the ferry, and 4.50 at an angle of 30.0 west of north relative to the water.

Question

What is the magnitude of the ferry's velocity relative to the water?

What is the direction of the ferry's velocity relative to the water?

How exactly do I do this? I've tried tan^-1(2400/1400) but I get it wrong.... =-(

Answer 1

Both velocities are vectors.
You could resolve each velocity into it's x- and y- components, which usually coincide with the East and North directions.
The velocity relative to water is the resultant, and the velocity of the ferry is yet unknown.
Velocity x-component y-component
1.6 0 1.6
? ? ?
------------------------------------
resultant =
4.5 4.5*cos(120) 4.5*sin(120)

From the table, it should be possible to find the individual components of the ferry by subtraction, and the velocity by vectorially summing the two components.
Post your answer for a check if necessary.