Magnitude and direction of ship relative to ground

AI Thread Summary
The discussion revolves around calculating the actual velocity of a ship navigating in a tidal current at Ambrose Channel, New York. The tidal current has a speed of 4.2 km/h directed 20 degrees south of east, while the ship moves at 16 km/h aimed due north. To determine the ship's velocity relative to the ground, a vector triangle approach is suggested, where the velocities are treated as vectors. Participants are encouraged to calculate the resultant vector's magnitude and direction based on the given parameters. The focus remains on applying vector addition to solve the problem effectively.
physicsquest
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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>
 
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physicsquest said:
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! :smile:

Relative velocities are vectors, so draw a vector triangle …

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

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