Question

Two forces with magnitudes of 150 and 100 pounds act on an object at angles of 40° and 170°, respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.

Answer 1

@dude

Answer 2

@Vocaloid

Answer 3

@Comerpickles

Answer 4

81.78 degrees

Answer 5

I need to show how i get it

Answer 6

Step by Step.

Answer 7

Okay. To solve, first split each force into x and y components.
F1 = 150

F1_x = 150 cos(40)
F1_y = 150 sin(40)

F1_x = 114.91
F1_y = 96.42

Now the second force:
F2 = 100

F2_x = 100 cos(170)
F2_y = 100 sin(170)

F2_x = -98.48
F2_y = 17.36

Notice that Force 2's x (horizontal) component is negative.
This means that it points to the left. If you draw out a diagram you'll see what I mean.

Now to solve for the resultant force:
FR = resultant force

FR_x = F1_x + F2_x
FR_y = F1_y + F2_y

FR_x = 16.43
FR_y = 113.78

What we have just solved for are the x and y components of the resulting force when the two forces are added together.
Now to find the magnitude and direction of the resultant force, use the following formulas.

Magnitude: use the distance formula
FR = sqrt[ (FR_x)^2 + (FR_y)^2 ]
FR = sqrt[ 13215.83 ]
FR = 114.96

Direction: remember that tangent of an angle gives its slope.
Since we have the slope and need the angle, we use arctangent.

Slope = rise / run = vertical / horizontal
=
FR_y / FR_x
=
6.93

Angle = arctangent(6.93)
=
81.78 degrees

Answer 8

Did you copy this or?

Answer 9

So i can make revisions lol

Answer 10

The step by step version yes because mainly I would need a graph to do this, which I do not have at the time

Answer 11

Ok thank you bro life freaking saver aha

Answer 12

Not really XD