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Two forces of 25 newtons and 85 newtons acting on a body form an angle of 55˚. Find the magnitude of the resultant force, to the nearest hundredth of a newton.

a. 88.26 N
b. 101.50 N
c. 92.92 N
d. 79.64 N

User Juhlila
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1 Answer

3 votes

Final answer:

The magnitude of the resultant force can be calculated using the law of cosines. Apply the formula R = √(F1² + F2² + 2 · F1 · F2 · cos(θ)) with the given forces and angle, and round the result to the nearest hundredth of a newton to find the correct choice.

Step-by-step explanation:

To find the magnitude of the resultant force when two forces act on a body at an angle, you can use the formula that comes from the law of cosines:

R = √(F1² + F2² + 2 · F1 · F2 · cos(θ))

Where R is the resultant force, F1 and F2 are the magnitudes of the two forces, and θ is the angle between them. For the forces of 25 newtons and 85 newtons forming a 55° angle:

R = √(25² + 85² + 2 · 25 · 85 · cos(55°))

Calculate the value to get the magnitude of the resultant force. Round the answer to the nearest hundredth to find the correct option from the given choices.

User Henk J Meulekamp
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