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.

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 Link

tutisto tutisto · Answer 2 · 2018-07-08T08:47:15+02:00

Magnitude:

[tex]v1= \ \textless \ 100cos50, 100sin50\ \textgreater \ [/tex] ⇒ [tex]v1= \ \textless \ 64.28, 76.6\ \textgreater \ [/tex]

[tex]v2=\ \textless \ 50cos160, 50sin160\ \textgreater \ [/tex] ⇒ [tex]v2=-46.98, 17.1\ \textgreater \ [/tex]

[tex]v1+v2 = \ \textless \ 17.3, 93.7\ \textgreater \ [/tex]
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°