Two forces with magnitudes of 200 and 100 pounds act on an object at angles of 60° and 170° respectively. Find the direction and magnitude of these forces. Round to two decimal places in all intermediate steps and in your final answer.
show work

- anonymous

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- anonymous

write something down if YOU want a medal

- anonymous

i just need help on the problem please!

- anonymous

plus I am sorry but I do not know the answer

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## More answers

- anonymous

calculate the vertical and horizontal components of each force, and then all the vertical forces together, then add horizontal forces together... after that u can combine the vertical and horizontal vector using pythagaros theorem to get the resulting force

- anonymous

im not sure how to do all that .. im horrible in math and im just trying to pass so i can be done:(

- anonymous

I know i have to resolve each vector into horizontal and vertical components using sin and cos but im not sure how to actually begin

- geerky42

Always try to sketch. It may help you.|dw:1359302063400:dw|

- geerky42

Just do what @Tushara told you to do.

- anonymous

i just dont know where or how to really do it :/

- mathstudent55

|dw:1359302350812:dw|

- geerky42

|dw:1359302341604:dw|\[\Large \sin \theta = \dfrac{y}{r} \Rightarrow r \sin \theta = y\]\[\Large \cos \theta = \dfrac{x}{r} \Rightarrow r \cos \theta = x\]

- anonymous

but how would i put this all into writing to show my work?
like in step form?

- mathstudent55

|dw:1359302475063:dw|

- anonymous

i began with this.. is this a good start;
f1x= 200cos(60)
f1x= 100 cos (170)
rx= 200 cos(60) + 100 cos(170)

- mathstudent55

F1 = 200, F2 = 100
F1x = F1 cos 60
F1y = F1 sin 60
F2x = f2 cos 170
F2x =F2 sin 170
Rx = F1x + F2x
Ry = F1y + F2y
R(theta) = tan^1(Ry/Rx)

- mathstudent55

On the second line, you mean f2x, but that's good.

- anonymous

but now where do i go
?

- mathstudent55

Now do the same for the force components in the y direction.

- anonymous

whhat do u mean?

- mathstudent55

Do this:
f1x= 200cos(60)
f2x= 100 cos (170)
rx= 200 cos(60) + 100 cos(170)
For F1y, F2y, and Ry

- mathstudent55

F1y = F1 sin 170
F2y = ...
Ry = F1y + F2y = ...

- anonymous

f1y = 100 sin (170)
f2y = 200 sin ( )
?? hmm

- mathstudent55

F1 = 200, F2 = 100.
You switched them.

- anonymous

f1 = 200 sin (170)
f2 = 100 sin (60)
??

- anonymous

okay the it would be ..

- mathstudent55

You got the x-components above and you did it correctly. Now you need the y-components.
f1y = 200 sin (60)
f2y = 100 sin (170)
Ry = f1y + f2y = 200 sin 60 + 100 sin 170

- anonymous

ok i got the 70 and 170 mixed around

- mathstudent55

There is no 70.

- anonymous

i mean 60*

- anonymous

sorry!

- mathstudent55

Remember the first force, F1, is 200 lb at 60 deg
The x component is F1x = 200 cos 60
The y component is F1y = 200 sin 60
The second force, F2, is 100 lb at 170 deg
The x component is F2x = 100 cos 170
The y component is F2y = 100 sin 170
The resultant's x-component is
Rx = F1x + F2x = 200 cos 60 + 100 cos 170
The resultant's y-component is
Ry = F1y + F2y = 200 sin 60 + 100 sin 170

- mathstudent55

Now you need to do the actual calculations with a calculator of what Rx and Ry are, and round off to 2 decimal places.

- anonymous

so all i have to do is put the equation in the calculator for rx and ry and thatll give me the answers?

- anonymous

i need to complete the problem?

- mathstudent55

For now, yes. That will give you the x- and y-components of the resultant.

- anonymous

okay .. and thats all i do then right

- anonymous

but i have to find the direction and magnitude?

- anonymous

??

- mathstudent55

Once you have the x- and y-components of the resultant, you need two more steps.
1. You need to find the magnitude of the resultant.
2. You need to find the direction of the resultant.

- anonymous

how do i do that?

- mathstudent55

For the magnitude of the resultant, you use the Pythagoras theorem.
For the direction of the resultant, you use the inverse tangent to get the angle.
See figure below:
|dw:1359304507660:dw|

- mathstudent55

yes

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