Question

WILL GIVE BRAINLEST ANSWER IF DONE IN 24 HRS Two forces with magnitudes of 150 and 100 pounds act on an object at angles of 40° and 170°, respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer. (pls show work)

Answer 1

Answer:

114.96 pounds at angle 81.76°

Step-by-step explanation:

Let i be the component along x-axis and j be the component along y-axis.

First force that is given is 150 acting at angle 40; $F1 = 150cos170i + 150sin40j = 114.91i +96.42j$

The second force 100 is acting at angle 170;

$F2 = 100cos170i + 100sin170j = -98.48i + 17.36j$

We now have the resultant force, which is: $114.91i + 96.42j + (-98.48i + 17.36j) = 16.43i + 113.78j$

Magnitude of resultant:

$\sqrt{16.43^{2} + 113.78^{2} }$ = 114.96 pounds

Angle it makes with horizontal; inverse tangent of $\frac{(113.78)}{(16.43)}$ = 81.76 degrees

Hope this helps; Brainliest appreciated!