Determine the x and y components of the following three vectors in the xy plane.
1) (a) A 14-m displacement vector that makes an angle of 22° clockwise from the +y direction.
x:
2) y:
3) (b) A 19-m/s velocity vector that makes an angle of 40° counterclockwise from the -x direction.
x:
4) y:
5) (c) A 48-lb. force vector that makes an angle of 169° counterclockwise from the -y direction.
x:
6) y:
1. 14m[22o] CW from +Y-axis.
X = 14*sin22 = 5.24 m.
2. Y = 14*Cos22 = 12.98 m.
3. 19m[40o] CCW from +X-axis.
X = 19*Cos40.
4. Y = 19*sin40
5. 48Lb[169o] CCW from -Y-axis = 48Lb[79o] N. of E.
X = 48*Cos79
6. Y = 48*sin79
To determine the x and y components of vectors in the xy plane, you can use trigonometry and the given information about the angles and magnitudes of the vectors.
Let's break down the process for each vector:
1) (a) For the 14-m displacement vector that makes an angle of 22° clockwise from the +y direction:
To find the x-component of the vector, you can use the formula: x = magnitude * cos(angle)
In this case, the magnitude is 14 m and the angle is 22° clockwise from the +y direction. So, x = 14 * cos(22°).
To find the y-component of the vector, you can use the formula: y = magnitude * sin(angle)
In this case, the magnitude is 14 m and the angle is 22° clockwise from the +y direction. So, y = 14 * sin(22°).
2) (b) For the 19-m/s velocity vector that makes an angle of 40° counterclockwise from the -x direction:
To find the x-component of the vector, you can use the formula: x = magnitude * cos(angle)
In this case, the magnitude is 19 m/s and the angle is 40° counterclockwise from the -x direction. So, x = 19 * cos(40°).
To find the y-component of the vector, you can use the formula: y = magnitude * sin(angle)
In this case, the magnitude is 19 m/s and the angle is 40° counterclockwise from the -x direction. So, y = 19 * sin(40°).
3) (c) For the 48-lb. force vector that makes an angle of 169° counterclockwise from the -y direction:
To find the x-component of the vector, you can use the formula: x = magnitude * cos(angle)
In this case, the magnitude is 48 lb and the angle is 169° counterclockwise from the -y direction. So, x = 48 * cos(169°).
To find the y-component of the vector, you can use the formula: y = magnitude * sin(angle)
In this case, the magnitude is 48 lb and the angle is 169° counterclockwise from the -y direction. So, y = 48 * sin(169°).
Now, you can substitute the values into the respective formulas to find the x and y components for each vector.