- #1

personguything

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## Homework Statement

Find the resultant of the following forces: (a) 30N at an angle of 40°, with respect to the x-axis, (b) 120N at an angle 135°, (c) 60N at an angle of 260°

The book's answer(and I'm assuming the correct one) is: 85.2N; 148 from +x axis

**2. The attempt at a solution**

*First I name each vector*

30N, 40 deg is a | 120N, 135 deg is b | 60N 260 deg is c

*Next I find the x and y components for each vector*

a

_{x}= 30*cos(40) = 23;

a

_{y}= 30*sin(40)

---

b

_{x}= 120*cos(35) = 98.3;

b

_{y}= 120*sin(35) = 68.8

---

c

_{x}= 60*sin(260) = -59.1;

c

_{y}= 60*cos(260) = -10.4

---

*Next I find the x and y components of the resultant vector*

R

_{x}= a

_{x}+b

_{x}+c

_{x}= 62.2

R

_{y}= a

_{y}+b

_{y}+c

_{y}= 62.2

*Next I find the hypotenuse(i.e. the magnitude of the resultant vector)*

R = √((62.2)^2+(77.7)^2) = 99.5

*And finally I calculate the angle of the resultant vector*

θ = arctan(77.7/62.2) = 51.3