Question
A vector is 0.888 m long and points in a 205 degree
direction.
Find the y- component of the vector.
direction.
Find the y- component of the vector.
Answers
GPT 3.5
To find the y-component of the vector, we need to use trigonometry.
First, we need to convert the direction angle (205 degrees) to radians.
In radians, 1 full revolution is equal to 2π radians. Therefore, 205 degrees is equal to (205/360) * 2π radians.
Using this formula, we can calculate the angle in radians as:
Angle in radians = (205/360) * 2π radians = (205/360) * 2 * 3.1416 radians ≈ 3.581 radians.
Now, we can use trigonometry to find the y-component of the vector.
The y-component can be found by multiplying the length of the vector (0.888 m) by the sine of the angle.
y-component = 0.888 m * sin(3.581 radians) ≈ 0.888 m * (-0.3599) ≈ -0.319 m.
Therefore, the y-component of the vector is approximately -0.319 m.
First, we need to convert the direction angle (205 degrees) to radians.
In radians, 1 full revolution is equal to 2π radians. Therefore, 205 degrees is equal to (205/360) * 2π radians.
Using this formula, we can calculate the angle in radians as:
Angle in radians = (205/360) * 2π radians = (205/360) * 2 * 3.1416 radians ≈ 3.581 radians.
Now, we can use trigonometry to find the y-component of the vector.
The y-component can be found by multiplying the length of the vector (0.888 m) by the sine of the angle.
y-component = 0.888 m * sin(3.581 radians) ≈ 0.888 m * (-0.3599) ≈ -0.319 m.
Therefore, the y-component of the vector is approximately -0.319 m.