# Homework Help: Find the resultant in unit-vector notation

1. Sep 28, 2008

### chanv1

1. The problem statement, all variables and given/known data

Three displacement vectors of a croquet ball are shown in the figure, where |a vector| = 22.0 units, |b vector| = 25.0 units, and |c vector| = 10.0 units.

(a) find the resultant in unit-vector notation

____ i hat + ____ j hat

(b) Find the magnitude and direction of the resultant displacement.
____ units
____ ° (from the +x axis)

2. Relevant equations

http://img214.imageshack.us/img214/1280/physicsqj6.th.jpg [Broken]http://g.imageshack.us/thpix.php [Broken]

3. The attempt at a solution

I'm completely stumped. Can someone please teach me how to start this problem? Thank you.

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Last edited by a moderator: May 3, 2017
2. Sep 28, 2008

### Integral

Staff Emeritus
This is very similar to the last problem I helped you with. Decompose each vector to x and y components. Add 'em all up.
A unit vector has magnitude 1 so you will need to "normalize" your result. That is divide each component by the magnitude of the resultant vector.

3. Sep 28, 2008

### chanv1

how do I get the resultant in unit-vector notation?

4. Sep 29, 2008

### chanv1

|a vector| = 22* cos 90 = 0 ; 22* sin 90 = 22
|b vector| = 25*cos 45 = 17.68 ; 25*sin 45 = 17.68
|c vector| = 10*cos -45 = 7.07 ; 10*sin -45 = -7.07

Fx = 24.75 Fy = 32.61

24.75^2 + 32.61^2 = c^2
c = 40.94

tan^-1 (32.61/24.75) = 52.80 degrees

(a) 24.75 i hat + 46.75 j hat
(b) 52.9 units; 62.10 degrees

Last edited: Sep 29, 2008