Physics...Vector math help...please??

Question

1. Find the resultant vector (value and angle) when the following two vectors are added together:
R1 = 22.4 m, θ = 26.6 degrees
R2 = 29.2 m, θ = 59 degrees

2. Find the resultant vector (value and angle) when the following two vectors are added together:
R1 = 40.3 m, θ = 7.1 degrees
R2 = 15.0 m, θ = -180 degrees


Answers:
1. |R| =
θ =
2. |R| =
θ =


***She gave us this link but i dont know how to use this thing... i am horrible at physics or anything to do with math related questions....

http://phet-web.colorado.edu/simulations/vectormath/vectorMath.swf

Answer 1

You are given
R___ Angle θ and components Rx and Ry
[Just go and 'grab 'one for now so let's do it manually ]

We know that
Rx= R cos(θ)
Ry= R sin(θ)

|R|=sqrt(Rv^2 + Ry^2)
θ=arctan (Ry/Rx)

Rx=Rx1+Rx2
Ry=Ry1+Ry2
_______________-now we are ready ____________
Rx= R1 cos(θ) + R2 cos(θ)
Rx= 22.4 cos(26.6) + 29.2 cos(59)
Rx= 20.0 + 15.0=35.0m
similarly
Ry=R1 sin(θ) + R2 sin(θ)
Ry=22.4 sin(26.6) + 29.2 sin(59)
Ry= 10.0 + 25.0
Ry=35.0 m

|R|=sqrt(35.0^2 + 35.0^2)=49.5 m
θ=arctan(Ry/Rx)= arctan(1)=45 deg

Do the same for problem 2. Pay attention to the signs. I would recommend to do it first graphically and then compare to calculations.

Have fun

Answer 2

The Component Method is a method that can be used to add two or more vectors. This method is based on the principle that any vector can be resolved or broken into two mutually perpendicular vectors which when added will give the original vector. The steps are as follows:
1) Get the x-component and the y-component of each vector using the appropriate trigonometric function (sine or cosine). Be sure to affix the proper sign of the component. This means that if the x-component is pointing to the right, usually we consider it positive; if it pointing to the left, we consider it negative. In the case of the y-component, if the y-component is pointing up, we usually consider it positive; if down we consider it as negative.
2) After this, we add all the x-components together, making sure that we consider the sign of each x-component in the addition. We do the same thing for the y-components. You can call the total or resultant of the x-components as Rx and that of the y-components as Ry. Remember to affix the proper sign of each resultant as revealed in your addition.
3) Next, we get the total resultant, Rt, of Rx and Ry
We use the Pythagorean Theorem to solve for Rt. Here, Rt is the hypotenuse, Rx and Ry are the legs of the right triangle.
(Rt)^2 = (Rx)^2 + (Ry)^2
Rt = sqrt[(Rx)^2 + (Ry)^2]
4. In this step we get the angle of the resultant using tangent function:
tangent A = (Ry)/(Rx)
A = arctan[(Ry)/(Rx)]
5. Write the complete answer:
Rt and angle A
So, let's apply the above steps to your problem.
Step 1:
R1 = 22.4 m, θ = 26.6 degrees
R1x = R1Cosθ
R1x = 22.4 m Cos 26.6 deg
R1x = +20.03 (pointing to the right)

R1y = R1Sin26.6 deg
R1y = 22.4 m Sin26.6 deg
R1y = +10.03 (pointing upward)

R2 = 29.2 m, θ = 59 degrees
R2x = R2 cosθ
R2x = 29.2mcos59deg
R2x = + 15.04 (pointing to the right)

R2y = R2sinθ
R2y = 29.2msin59deg
R2y = + 25.03 (pointing upward)

Step 2:
Rx = R1x + R2x
Rx = 20.03 + 15.04
Rx = 35.07

Ry = R1y + R2y
Ry = 10.03 + 25.03
Ry = 35.06

Step 3:

Rt = sqrt[(Rx)^2 + (Ry)^2]
Rt = sqrt[35.07^2 + 35.06^2]
Rt = 49.59

Step 4:
A = arctan[(Ry)/(Rx)]
A = arctan[35.06/35.07]
A = 44.99 or 45 deg.

Step 5:
Rt = 49.59 m east 45 deg north ANS.

Hope I help.

teddyboy

Answer 3

First convert from polar form to rectangular and then sum the x and y components x1=40.3cos7.1
y1=40.3sin7.1
x2=15cos[-180]
y2=15sin[-180]

After you sum the components the magnitude is the sqrt of the sum of their squares and the angle arctan[y/x]