Final answer:
To find the value of the expression G = A + 2B - F, we use the given magnitudes and direction angles of A, B, and F. By calculating the components of A, B, and F along the x and y axes, we can find the components of G. Using the Pythagorean theorem and inverse tangent function, we can find the magnitude and direction angle of G.
Step-by-step explanation:
To find the value of the expression G = A + 2B - F, where A, B, and F are displacement vectors, we need to use the magnitudes and direction angles of A, B, and F. Given the magnitudes A = 10.00, B = 7.00, and F = 20.00, and the direction angles a = 35°, B = -110°, and p = 110°, we can use the trigonometric functions to find the components of A, B, and F along the x and y axes. Then, we add the components of A, 2B, and -F to find the components of G along the x and y axes. Finally, we use the Pythagorean theorem to find the magnitude of G and the inverse tangent function to find the direction angle of G.
Using the given values, we can calculate the components of A, B, and F as follows:
Ax = Acos(a) = 10.00cos(35°) = 8.15 cm
Ay = Asin(a) = 10.00sin(35°) = 5.74 cm
Bx = Bcos(B) = 7.00cos(-110°) = 3.50 cm
By = Bsin(B) = 7.00sin(-110°) = -6.31 cm
Fx = Fcos(p) = 20.00cos(110°) = -9.85 cm
Fy = Fsin(p) = 20.00sin(110°) = 18.14 cm
Next, we calculate the components of G:
Gx = Ax + 2Bx - Fx = 8.15 + 2(3.50) - (-9.85) = 25.15 cm
Gy = Ay + 2By - Fy = 5.74 + 2(-6.31) - 18.14 = -31.60 cm
Using the Pythagorean theorem, we can find the magnitude of G:
G = sqrt(Gx^2 + Gy^2) = sqrt((25.15)^2 + (-31.60)^2) = 40.28 cm
Finally, we can find the direction angle of G using the inverse tangent function:
0G = atan(Gy / Gx) = atan(-31.60 / 25.15) = -51.72°
Therefore, the value of G is 40.28 cm and the direction angle of G is -51.72°.