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

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Answer 2

Magnitude = 95.29 pounds

Direction = 79.54 degrees

Explanation:

Resolve forces into x and y components.

x-component

= 100 cos(50) + 50 cos(160)

= 64.28-46.98

= 17.29

y-component

= 100 sin(50) + 50 sin(160)

= 76.60 + 17.10

= 93.71

Magnitude

= sqrt(x^2+y^2)

= sqrt(17.29^2+93.71^2)

= 95.29

Angle = arctangent(93.71/17.29) = 79.54 degrees