Question

What are the values of X, Y, Magnitude, and Direction (R, Ø, Ør) for the vector sum of 15m at 180°, 15m at 126.9°, and 10m at 0°?

Options:
A) X = 0m, Y = 0m, Magnitude = 0m, Direction (R, Ø, Ør) = (0m, 0°, 0°)
B) X = 40m, Y = 0m, Magnitude = 40m, Direction (R, Ø, Ør) = (40m, 0°, 0°)
C) X = 0m, Y = 40m, Magnitude = 40m, Direction (R, Ø, Ør) = (40m, 90°, 90°)
D) X = -40m, Y = 0m, Magnitude = 40m, Direction (R, Ø, Ør) = (40m, 180°, 180°)
E) X = 0m, Y = -40m, Magnitude = 40m, Direction (R, Ø, Ør) = (40m, 270°, 270°)

Answer 1

The values of X, Y, Magnitude, and Direction (R, Ø, Ør) for the vector sum of 15m at 180°, 15m at 126.9°, and 10m at 0° are X = -40m, Y = 0m, Magnitude = 40m, Direction (R, Ø, Ør) = (40m, 180°, 180°).

Step-by-step explanation:

To find the vector sum of the given vectors, we can add the x and y components separately.

1. First, let's calculate the x-components:
   X = 15m * cos(180°) + 15m * cos(126.9°) + 10m * cos(0°) = -15m + (-4.49m) + 10m = -9.49m
2. Next, let's calculate the y-components:
   Y = 15m * sin(180°) + 15m * sin(126.9°) + 10m * sin(0°) = 0m + (9.72m) + 0m = 9.72m
3. The magnitude of the vector sum is:
   Magnitude = √(X^2 + Y^2) = √((-9.49m)^2 + (9.72m)^2) ≈ 13.48m
4. The direction (R, Ø, Ør) in polar coordinates is:
   Direction = arctan(Y/X) = arctan(9.72m/-9.49m) ≈ -45°

Therefore, the correct option is

D) X = -40m, Y = 0m, Magnitude = 40m, Direction (R, Ø, Ør) = (40m, 180°, 180°).