Question

Magnitudes and directions of vectors.

Answer 1

The magnitudes and directions of two forces acting at a point p are given. Approximate the magnitude and direction of the resultant vector, accurate to two decimal places
a) 5.00lb, 200 degrees
b) 7.00lb, 65 degrees.

Answer 2

@jim_thompson5910 :P can we do this one?

Answer 3

find the component <x,y> form of each vector

then you can add up the vectors component-wise

Answer 4

x = r*cos(theta)
y = r*sin(theta)

Answer 5

Where do I derive the r from?

Answer 6

r = distance from origin to vector tip

r = magnitude of vector (ie force applied)

Answer 7

so 5 for part a
a) would be
5cos(200)
5sin(200)
?

Answer 8

yes

Answer 9

a = <-4.698,-1.710>

Answer 10

b= <2.958,6.344>

Answer 11

and when I add those up I get
= <-1.74,4.63>

Answer 12

they want it "accurate to two decimal places"

Answer 13

...that's what I did o.0

Answer 14

oh, I didn't do a and b accurate to two decimal places but that's because that's part of the process to get to the final answer and should be more accurate I think (hence more decimal places)
but the final answer is ok, yeah?

Answer 15

hmm maybe they just want the final answer to 2 decimal places, the steps just leave it to 15 or so (let the calculator handle it)

Answer 16

haha k. final answer looks good though? :)

Answer 17

yes it looks perfect. I'm getting the same

Answer 18

oh wait

Answer 19

they don't want the <x,y> form of the resultant

they want the "magnitude and direction of the resultant vector"

Answer 20

ou.

Answer 21

r = magnitude
theta = direction

r = sqrt(x^2 + y^2)

theta = arctan(y/x) will give you the angle, but it will say some angle in Q4. Add on 180 degrees to move the angle to Q2

<x,y> = <-1.74,4.63> is in Q2

Answer 22

so magnitude: 4.95

Answer 23

yes