How Do You Calculate a Boat's Relative Velocity with a Current Using Cosine Law?

AI Thread Summary
To calculate a boat's relative velocity with a current using the cosine law, the boat's heading and speed, along with the current's direction and speed, must be accurately defined. In this case, the boat heads 15° west of north at 3 m/s, while a current flows at 2 m/s from 40° east of north. The angle between the two vectors was determined to be 125°, leading to a calculated resultant velocity of 4.459 km/h. However, the correct answer is noted to be 2.5 m/h if the current's direction is reversed. Accurate vector analysis is crucial for determining the resultant velocity.
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Homework Statement



2. A boat heads 15° west of north witha water speed of 3m/s. Determine its velocity relative to the ground when there is a 2m/s current from 40° east of north.



Homework Equations



cosine law

The Attempt at a Solution




I found the angle between the two vectors to be 125 and then used cosine law and gor the resultant velicity as 4.459 km/ h but the ans. is 2.5 m/h
 
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a.a said:
I found the angle between the two vectors to be 125 and then used cosine law and gor the resultant velicity as 4.459 km/ h but the ans. is 2.5 m/h

Hi a.a! :smile:

2.5 is the right answer if the current is the other way round. :confused:
 

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