ACTIVITY 3.10
ADDING TWO VECTORS IN POLAR FORM

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Given two vectors in polar form= U and= V , how will we make his sum? You remember that, depending on we have seen in previous activities, the module of the two vector sum it isn't the  sum of the modules (nor the argument adds of its arguments, observe the figure).

To make this sum, we do not have more remedy than start by calculating his components:

= U = (UCos, USin)
= V = (VCos, VSin)

make the sum:+ = (UCos+ VCos, USin+ VSin)

and finally, if we want to give the result in polar form, calculate the module and the argument of the sum:

(You think about adding 180 º to Atan if+ It is in the 2nd or 3rd quadrant, that is to say, if the 1rst component of+is negative).

INTERACTIVE ACTIVITY

A boat must move by a canal with the help of two forcesand of 3 kN and 4 kN respectively. You try to get the arguments of these two forces so the boat moves by the canal on straight along. You try to get it in the three following forms:

1) Without varying the forceand modifying the direction of the force (moving the end only of the force).

2) You update this web page and repeat the exercise now without varying the forceand modifying the direction of the force.

3) You update the web page again and repeat the exercise varying the two forces simultaneouslyand.

 SOLUTION

HOMEWORK
(Do you want a Word document prepared for making this work?)

a) You calculate the module and the arguments of  the three following vectors sum =2 30º, =3 135º and =4 270º.

b) We walk 4 km in straight and in NE direction, after 6 km more in straight and in NO direction, and finally 8 km also calculates in straight and in S. direction. Calculate how many km have moved us away from the starting point?

END OF ACTIVITY 3.10
ADDING TWO VECTORS IN POLAR FORM

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