find displacement 4 vectors (1) 40 meters @10, (2) 30 meters @ 190 and (1)50 meters @ 280
To find the displacement using the given 4 vectors, we need to add the vectors together. Each vector consists of a magnitude (the distance) and a direction.
Let's break down each vector:
1) 40 meters @ 10 degrees: This means the vector has a magnitude of 40 meters and is directed at an angle of 10 degrees from the reference direction (usually the x-axis). We can represent this vector as (40 @ 10).
2) 30 meters @ 190 degrees: This vector has a magnitude of 30 meters and is directed at an angle of 190 degrees from the reference direction. We can represent it as (30 @ 190).
3) 50 meters @ 280 degrees: This vector has a magnitude of 50 meters and is directed at an angle of 280 degrees from the reference direction. We can represent it as (50 @ 280).
Next, we need to convert the polar coordinates (magnitude and direction) into Cartesian coordinates (x and y coordinates). To do this, we can use the following trigonometric formulas:
x = magnitude * cos(direction)
y = magnitude * sin(direction)
Using these formulas, we can find the x and y components of each vector:
1) (40 @ 10):
x = 40 * cos(10) ≈ 39.66 meters
y = 40 * sin(10) ≈ 6.94 meters
2) (30 @ 190):
x = 30 * cos(190) ≈ -29.15 meters
y = 30 * sin(190) ≈ -9.80 meters
3) (50 @ 280):
x = 50 * cos(280) ≈ -41.42 meters
y = 50 * sin(280) ≈ -19.04 meters
Now, we can find the resultant vector by adding the x and y components of each vector:
Resultant x = 39.66 - 29.15 - 41.42 ≈ -30.91 meters
Resultant y = 6.94 - 9.80 - 19.04 ≈ -21.90 meters
Finally, we can represent the resultant vector as its magnitude and direction:
Magnitude = √((-30.91)^2 + (-21.90)^2) ≈ 37.44 meters
Direction = arctan(Resultant y / Resultant x) ≈ -138.69 degrees
Therefore, the displacement vector is approximately 37.44 meters @ -138.69 degrees.