find the direction and magnitude of the resultant force.

Question

two forces with magnitudes of 90 and 50 pounds act on an object at angles of 30 and 160, respectively. find the direction and magnitude of the resultant force.

Answer 1

Step 1:

Magnitude of the two forces are  lb and  lb.

Two forces acting on an object at an angles of  and .

Find the horizontal and vertical components of .

Horizontal component of vector  is 

Vertical components of vector  is .

Therefore,   and .

 and 

Write the force  in vector form.

Substitute corresponding values.

.

Write the force  in vector form.

Substitute corresponding values.

.

Resultant force vector .

.

Step 2:

Find the magnitude and direction of the resultant force .

Magnitude of vector  is .

Direction angle of the vector  is .

Thus, 

.

Direction angle of the resultant  vector is  .

.

Direction angle of the resultant force is .

Magnitude of the resultant force is  lb.

Solution:

Magnitude of the resultant force is  lb.

Direction angle of the resultant force is .