Sure! To calculate the x and y components of the vector, we will use trigonometry.
Step 1: Understand the vector in question
The magnitude of the vector given is 17 m/s² and the vector is 38 degrees counterclockwise from the -y-direction (or to the left of the -y-axis).
Step 2: Convert degree to radian
Trigonometric functions in mathematics use angles in radian, not in degrees, so it is ideal to convert the angle from degrees to radian. By definition, π radian is equal to 180 degrees. Therefore,
38 degrees * (π / 180) = 0.6632 radians.
Now, we have the magnitude of the vector being 17m/s^2 and the angle is 0.6632 radians left of -y-axis.
Step 3: Calculate x and y components using trigonometry
The x and y components of the vector can be calculated using the definitions of sine and cosine in relation to a right triangle.
For the x-component, because it's pointing to the left of the -y-axis we will be treating it as a negative value and we'll use the sine of the angle instead of the cosine.
x = -Magnitude * sine(angle) = -17 m/s² * sin(0.6632 rad) = -10.466 m/s²
For the y-component, we have to use cosine because this is based on the -y-axis, and since it's a -y direction, we're keeping it negative.
y = - magnitude * cosine(angle) = -17 m/s² * cos(0.6632 rad) = -13.396 m/s²
Summarizing, The x-component of the vector a is -10.466 m/s² and the y-component of the vector a is -13.396 m/s².