Question

Two forces with magnitudes of 100 and 50 pounds act on an object at angles of 50° and 160°, 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

The resultant force is the sum of all forces positioned at different directions and placed in a specific angle. In this case, we can take the short way to answer this problem. we use the calculator and shift the mode to complex to add 100<50 and 50<160. the answer is 95.29<79.54. The magnitude is 95.29 pounds and the angle is 79.54°.

Answer 2

Magnitude:

$v1= \ \textless \ 100cos50, 100sin50\ \textgreater$ ⇒ $v1= \ \textless \ 64.28, 76.6\ \textgreater$

$v2=\ \textless \ 50cos160, 50sin160\ \textgreater$ ⇒ $v2=-46.98, 17.1\ \textgreater$

$v1+v2 = \ \textless \ 17.3, 93.7\ \textgreater$
the magnutude of this vector is 95.29 pounds

Direction:

To find the direction you can do 17.3=|v| cosθ and the magnitude of the vector (|v|) was already found to be 95.29 so now solve for theta (θ), use your calculator and you get the angle θ=79.52°