Let forces A and B be as shown in the diagram. If C newtons (N) is the magnitude of the resultant force, calculate C correct to the nearest whole number. (Hint: Use the Cosine Rule with the resultant vector C=A+ B)
A= 1200N
B=1400N
angle in between is 155
To find the magnitude of the resultant force, C, we need to use the cosine rule with the vectors A and B.
The cosine rule states that for any triangle with sides a, b, and c, and angle C opposite side c, the following equation holds true:
c^2 = a^2 + b^2 - 2ab * cos(C)
In this case, A and B are the sides of the triangle, and the angle in between them is 155 degrees. Let's substitute the given values into the formula.
A = 1200 N
B = 1400 N
angle C = 155 degrees
Using the cosine rule, we have:
C^2 = 1200^2 + 1400^2 - 2(1200)(1400) * cos(155)
Now, let's calculate the value of C:
C^2 = 1440000 + 1960000 - 3360000 * cos(155)
C^2 = 3400000 - 3360000 * cos(155)
To get the value of C, we need to find the square root of the right side of the equation. Let's calculate it.
C = √(3400000 - 3360000 * cos(155))
Using a calculator, we can evaluate this expression:
C ≈ 2026.27
Rounding this value to the nearest whole number, we get:
C ≈ 2026
Therefore, the magnitude of the resultant force, C, is approximately 2026 Newtons (N).