The magnitude of vector is 40.0 units and points in the direction 315° counterclockwise from the positive x-axis. Calculate the x- and y-components of this vector.
y=r sin theta
y= 40*sin315
y=-28.3 units
x=r cos theta
x= 40*cos315
x=28.3 units
To calculate the x- and y-components of the vector, you need to use trigonometry.
First, let's determine the angle in radians. The angle is given as 315° counterclockwise from the positive x-axis. To convert to radians, we multiply by π/180:
Angle in radians = 315° * (π/180) = 7π/4 radians
Next, we can use this angle to find the x- and y-components of the vector.
x-component = magnitude * cos(angle)
y-component = magnitude * sin(angle)
Given:
Magnitude of the vector: 40.0 units
Angle in radians: 7π/4 radians
Now, we can substitute these values into the formulas:
x-component = 40.0 * cos(7π/4)
y-component = 40.0 * sin(7π/4)
Calculating the x-component:
x-component = 40.0 * cos(7π/4)
= 40.0 * cos(315° * (π/180))
= 40.0 * cos(7π/4)
≈ 28.3 units
Calculating the y-component:
y-component = 40.0 * sin(7π/4)
= 40.0 * sin(315° * (π/180))
= 40.0 * sin(7π/4)
≈ -28.3 units
Therefore, the x-component of the vector is approximately 28.3 units, and the y-component is approximately -28.3 units.