This is a Physics problem, however I decided to post it in Mathematics to garner more help :).

A motorboat heads due west at 13 m/s relative to a river that flows due north at 5.0 m/s. What is the velocity (both magnitude and direction) of the motorboat relative to the shore?

I got 16.9 m/s at 57 degrees. I'm not sure if I'm right. Any help would be greatly appreciated :).

Question

This is a Physics problem, however I decided to post it in Mathematics to garner more help :).

A motorboat heads due west at 13 m/s relative to a river that flows due north at 5.0 m/s. What is the velocity (both magnitude and direction) of the motorboat relative to the shore? 

I got 16.9 m/s at 57 degrees. I'm not sure if I'm right. Any help would be greatly appreciated :).

anonymous · Answer

Yerrrrr right!!!!

anonymous · Answer

This is a vector problem. 
The '^' symbol denotes a power, ('4^2' is '4 squared')

letterstowords · Answer

Are you positive I am right? :)

anonymous · Answer

The first step is to break down the components of the NorthWest motion (13 m/s). The phrase Northwest means it has an angle of 45 degrees north of west. So both the north and west components will be equal. 
Pythagorean theorem: A^2 + B^2 = C^2 
We have C^2, it is 13^2 which is 169. 
Divide that by two to get the squares of one of the components: 84.5,. 
The square root of 84.5 is 9.19. 

So the components of the Northwest motion at 13 m/s is 
9.19 m/s north and.. 
9.19 m/s west. 

Add the north motion of the boat relative to the water to the motion of the water (north at 5 m/s) 
9.19+5= 14.19 m/s North. 

Our new vector components are 
14.19 m/s North and 
9.19 m/s West. 
Pthagorean theorem again tells us the magnitude of the motion: 
14.19^2 + 9.19^2 = C^2 = 285.81 
Take the square root and get 16.9 m/s 

Now we have a vector triangle. 

Opposite wall: 14.19 
Adjacent Wall: 9.19 
Hypotenuse: 16.9 
we need the angle in the bottom right corner: 
(angle)= opposite / hypotenuse = 14.19/16.9 
(angle)= .8396449704 
ArcSin(.8396449704) = 57.1 degrees 

The magnitude and direction: 
16.9 m/s at 57 degrees North of West.

anonymous · Answer

Absolutely! :)

letterstowords · Answer

Haha that's from Yahoo! answers. My problem is a bit different than that. However, the answers are the same, which is weird. Someone also told me the degree is not 57 but 33. So, that's why I'm not sure if I am right.

primeralph · Answer

Owned.
@shelbygt520

anonymous · Answer

yes haha I try to use my brain as little as possible if its on google... SHUT UP Ralph you meanie @primeralph

letterstowords · Answer

Hahah, @primeralph.

anonymous · Answer

I'm pretty sure you're right but you are going to make me use my brain I see lol

phi · Answer

the problem says
motorboat heads due west at 13 m/s relative to a river 
river flows 5 m/s  due north|dw:1394315254068:dw|