Magnitude and direction of ship relative to ground

[physicsquest]

Homework Statement

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?

Homework Equations

vx= vtx-vsx
vy= vty-vsy
tan$$\phi$$= $$\sqrt{(v<span style="font-size: 9px">x^2 + v<span style="font-size: 9px">y^2)}<br /> tan\phi=v<span style="font-size: 9px">y/v<span style="font-size: 9px">x<br /> <br /> <br /> <br /> <h2>The Attempt at a Solution</h2><br /> </span></span></span></span>$$

 

[tiny-tim]

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?

Hi physicsquest!

Relative velocities are vectors, so draw a vector triangle …

what is the length and direction of the third side? ​