Given that Force 1 = 70 pounds and Force 2 = 120 pounds , find the angle between the forces if the magnitude of the resultant force is 90 pounds . Round answer to the nearest
degree.
A) 48° B) 40° C) 53° D) 45° E) 60°
I think it is answer B
To find the angle between two forces, you can use the formula:
Cosine(theta) = (Force 1 dot product Force 2) / (magnitude of Force 1 * magnitude of Force 2)
First, calculate the dot product of Force 1 and Force 2. The dot product is calculated as:
Force 1 dot product Force 2 = (Force 1 magnitude) * (Force 2 magnitude) * cosine(theta)
Now, we have the dot product of Force 1 and Force 2, which is given by:
Force 1 dot product Force 2 = (70 pounds) * (120 pounds) * cosine(theta)
Next, calculate the magnitude of the resultant force:
Magnitude of the Resultant Force = 90 pounds
Finally, rearrange the equation:
cosine(theta) = (Force 1 dot product Force 2) / (magnitude of Force 1 * magnitude of Force 2)
Substituting the values, we get:
cosine(theta) = ((70 pounds) * (120 pounds)) / ((90 pounds) * (120 pounds))
cosine(theta) = 84,000 / 10,800
cosine(theta) = 7.78
Now, we can find the value of theta by taking the inverse cosine (also known as arccos) of 7.78:
theta = arccos(7.78)
However, the value of 7.78 is greater than 1, which is not possible for the cosine function. Therefore, there has been an error in one of the calculations or the given values. Please double-check your question or provide additional information.