# Vector addition and Relative motion

1. Sep 27, 2011

1. The problem statement, all variables and given/known data
1) A boy is floating on a raft in a river. THe water flows at a speed of 12m/s east. The boy's feet kick the water,causing a velocity of 2m/s at an angle of 43 degrees north of east. Using Vector components, calculate the magnitude of the raft's velocity.

2)One vector has a magnitude of 20m/s and acts an angle of 25 degrees. The next vector has a magnitude of 12m/s and acts at an angle of 120 degrees. The final vector acts at an angle of 70 degrees and has a magnitude of 14m/s. Calculate the magnitude and the angle of the resultant vector.
2. Relevant equations
1) 12xtan(43)= 11.19m/s

2)20m/s + 12m/s+ 14m/s = 46m/s????????
25degree+ 120+ 70= 215degree.........

3. The attempt at a solution
1) 11.19m/s
2)46m/s and 215 degree???

2. Sep 27, 2011

### lewando

Hello nadong2dong, welcome to PF! For part 1 (assuming east is +x and north is +y), the x-component of the river is clearly 12 m/s, and the y-component of the river is clearly 0 m/s. What x and y components can you come up with for the vector caused by the boy's kicking?

Last edited: Sep 27, 2011
3. Sep 27, 2011

uhhh i dont quite understand what you are talking about

4. Sep 27, 2011

I get that x is 12 and y is 0, but what should i do to foind components caused by the boy's kicking
?

5. Sep 27, 2011

2sin(43)
2cos(43)?

6. Sep 27, 2011

### lewando

Do you get what the term "vector components" means?

7. Sep 27, 2011

### lewando

Sure, but which is the x component? Which is the y component??

8. Sep 27, 2011

cos is the x component
and sin is the y?

9. Sep 27, 2011

It is very hard for me to picture the question in my mind.

10. Sep 27, 2011

### lewando

Why don't you draw a vector diagram of what is going on?

11. Sep 27, 2011

that is the problem, i cant really draw a vector diagram for this question

12. Sep 27, 2011

### lewando

Are you sure? Why the question mark? You happen to be right. Make sure you understand why you are right.

13. Sep 27, 2011

ok i got 13.53 m/s

Is that right?

14. Sep 27, 2011

### lewando

That looks right, how did you get there?

15. Sep 27, 2011

square root of (2sin43)^2 + (2cos43 +12)^2

16. Sep 27, 2011

### lewando

Alright, good work by you!

Well, [drawing vector diagrams] are fundamental to the solution of part 2. You should understand this this as soon as possible.

If your textbook does not cover this, get another textbook or search for online resources such as:

I'm done for the night. If someone else does not jump in, let's continue this later.

Last edited by a moderator: Sep 25, 2014
17. Sep 27, 2011