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

[a.a]

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

 

[tiny-tim]

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!

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

 

[Moetasim]

Your approach to finding the relative velocity of the boat is correct. However, there may be a mistake in your calculations as the correct answer should be 3.9 m/s, not 2.5 m/s. Please double check your calculations to ensure accuracy. Additionally, make sure to include units in your final answer as it should be in meters per second, not kilometers per hour. Keep up the good work in applying the cosine law to solve for relative velocities!