Question

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. (5 points)

Answer 1

114.96 Pounds and 81.78 Degrees

Answer 2

Resultant force = 114.96 pounds at angle 81.76°

Explanation:

Let i be the component along X axis and j be the component along Y axis.

First force 150 is acting at angle 40°.

`F_1=150cos40i+150sin40j=114.91i+96.42j`

Second force 100 is acting at angle 170°.

`F_2=100cos170i+100sin170j=-98.48i+17.36j`

Resultant force = 114.91i+96.42j + (-98.48i+17.36j) = 16.43 i + 113.78 j

Magnitude of resultant
`=√(16.43^2+113.78^2)` = 114.96 pounds

Angle it makes with horizontal
`=tan^(-1)\left ( (113.78)/(16.43) \right )=81.76^0`