MHB What is the resultant force and angle for two forces acting on an object?

[RobertoPink]

A 100 pound force and a 150 pound force act on an object. If the angle between the force 40 degress, find the magnitude of the resultant force and the angle the resultant force makes with the 150 pound force.

 

[skeeter]

A 100 pound force and a 150 pound force act on an object. If the angle between the force 40 degress, find the magnitude of the resultant force and the angle the resultant force makes with the 150 pound force.

let the 150 lb force be directed along the positive x-axis and the 100 lb force be directed 40 deg relative to the positive x-axis in quadrant I (recommend you make a sketch)

using the method of components in the x and y directions, $R$ represents the resultant vector, $\theta$ is the resultant vector's direction relative to the positive x-axis ...

$R_x = 150 + 100\cos(40)$

$R_y = 0 + 100\sin(40)$

$|R| = \sqrt{R_x^2+R_y^2}$

$\theta = \arctan\left(\dfrac{R_y}{R_x}\right)$