Find the direction and magnitude of the resultant forces

[dancer1311]

1. Two forces of magnitude 25 pounds and 40 pounds act on an object. The force of 40lb acts along the positive x-axis, and the force of 25lb acts at an angle of 80 degrees with the positive x-axis. Find the direction and magnitude of the resultant force. Round the direction and magnitude to the nearest whole number.



2. The answer is suppose to be direction: 29 degrees and magnitude 51lb



3. i thought it was suppose to be 65(cos30i + sin30j)
which got me 65\sqrt{}3 divided by 2 i plus 65 divded by 2
but this doesn't give me the correct answers.

 

[rootX]

From where you are reaching at "65(cos30i + sin30j)"?

<40,0> + <other force vector_x, other force vector_y> = ?

 

[mugaliens]

F1: 40 lbs, along x-axis

F2: 25 lbs, 80 degrees from x-axis.

Separating out the components, we have:

x-axis component = 40 + 25*cos(80) = 40 + 4.34 = 44.34 lbs

y-axis component = 25*sin(80) = 24.62 lbs

Net force = sqrt( x^2 + y^2) (you can do the math) and the angle is tan^-1*(24.62/44.34).

 

[HallsofIvy]

Since both rootX and mugaliens divided into components, here is a direct way: draw the 25 lb force as starting at the tip of the 40 lb force and you have a triangle with sides of length 25 and 40 and angle between them 180- 80= 100 degrees. Use the "cosine law" to find the length of the third side, the magnitude of the resultant force, and use the "sine law" to find the angle that third side makes with the 40 lb force.