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3 years ago

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Two forces with magnitudes of 150 and 100 pounds act on an object at angles of 30° and 120°, respectively. Find the direction an

d magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.

1 answer:

anyanavicka [17]3 years ago

3 0

Answer:

Resultant = 180.27 pounds

direction is 63.69 degrees

Step-by-step explanation:

We have to resolve the x and y component of both forces with respect to given angles

Fx = 150cos30 +100cos120

= 150(0.866)+100(-0.5) =129.9-50=79.9 pounds

and

Fy= 150sin30+100sin120

= 150(0.5) +100(0.866)= 75+ 86.6 =161.6 pounds

Magnitude of the resultant is = $\sqrt{Fx^2+Fy^2}$

= $\sqrt{(79.9)^2+(161.6)^2}$

= 180. 27 pounds

Direction of the resultant is given by arctan( $\frac{Fy}{Fx}$

arctan( $\frac{161.6}{79.9}$

=63.69 degrees

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