# Magnitude and direction of ship relative to ground

1. Sep 22, 2009

### physicsquest

1. The problem statement, all variables and given/known data
At the entrance of Ambrose Channel at New York harbor, the tidal current at one time of the day has a velocity of 4.2 km/h in a direction 20 degrees south of east. Consider a ship in this current; suppose that the ship has a speed of 16 km/h relative to the water. If the helmsman keeps the bow of the ship aimed due north, what will be the actual velocity (magnitude and direction) of the ship relative to the ground?

2. Relevant equations
vx= vtx-vsx
vy= vty-vsy
tan$$\phi$$= [tex]\sqrt{(vx^2 + vy^2)}
tan\phi=vy/vx

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Sep 23, 2009

### tiny-tim

Hi physicsquest!

Relative velocities are vectors, so draw a vector triangle …

what is the length and direction of the third side?