Calculating Powerboat Velocity Across Moving River

[helpneeded01]

This question is confusing, can someone please help me on this question.
A powerboat heads due northwest at 10 m/s relative to the water across a river that flows due north at 4.2 m/s. What is the velocity (both magnitude and direction) of the motorboat relative to the shore?
How would I find the velocity and the degrees west of north?

 

[helpneeded01]

This question is confusing, can someone please help me on this question.
A powerboat heads due northwest at 10 m/s relative to the water across a river that flows due north at 4.2 m/s. What is the velocity (both magnitude and direction) of the motorboat relative to the shore?
How would I find the velocity and the degrees west of north?

 

[Astronuc]

This is a vector sum problem.

One adds the two vectors velocity of the boat 10 m/s at 45° from north with respect to water, and 4.2 m/s (velocity with respect to shoreline) due north (river flows north). Find the resultant vector and the angle with respect to north, then component of velocity due north. Think scalar product.

 

[helpneeded01]

im still not getting this...

 

[Astronuc]

Please refer to these examples of relative motion and please read about vector addition if that concept is not clear.

http://hyperphysics.phy-astr.gsu.edu/hbase/relmot.html#c2


Then please write the velocity vector for the boat with respect to water, i.e. 10 m/s due NW. Then write the velocity vector for the river flow, 4.2 m/s due N.

Then find the sum (resultant vector). Let unit vector i point due E, so -i points due west, and take unit vector j as pointing due north.

Then knowing the resultant vector, find its magnitude and the angle with respect to north.

 

[helpneeded01]

thank you very much :)

 

[jdogg0075]

Assuming when you say "due northwest" meaning 45 degrees west of north. Using this then we can set up vectors to solve this. One of your vectors is 10 m/s at 45 degrees north of west and another is at 4.2 m/s north or 0 degrees. Using law of cosines you can use this information to solve for your resulting vector. This was my equation for law of cosines
C=$$\sqrt{10^{2}+4.2^{2}-2*10*4.2*cos(135)}$$

 

[helpneeded01]

how would you find the angle west of north?