a vector has a magnitude of 3.5 m and points in a direction that is 145 degrees below the x axis.find the x and y component of this vector
145 degrees below the x-axis? Really? 90 degrees would be pointing straight down!
That's pointing backwards.
In any case, the components would be
x = 3.5 cos theta
y = 3/5 sin theta
where theta is measured from the x-axis.
Hint: DRAW THE VECTOR!
145o below +x-axis = 360-145 = 215o CCw.
V = 3.5m[215o].
X = 3.5*Cos215 =
Y = 3.5*sin215 =
To find the x and y components of a vector with magnitude and direction, we can use trigonometry.
Given:
Magnitude of the vector = 3.5 m
Direction = 145 degrees below the x-axis.
Let's define our coordinate system with the positive x-axis to the right and the positive y-axis upwards.
Step 1: Find the x-component.
To find the x-component, we can use the cosine function. The cosine of an angle gives us the ratio of the adjacent side to the hypotenuse.
x-component = magnitude * cosine(angle)
x-component = 3.5 m * cosine(145 degrees)
x-component = 3.5 m * cos(145 degrees)
Using a calculator, we find that cos(145 degrees) is approximately -0.5736.
x-component ≈ 3.5 m * (-0.5736) ≈ -2.01 m (rounded to two decimal places)
Therefore, the x-component of the vector is approximately -2.01 m.
Step 2: Find the y-component.
To find the y-component, we can use the sine function. The sine of an angle gives us the ratio of the opposite side to the hypotenuse.
y-component = magnitude * sine(angle)
y-component = 3.5 m * sine(145 degrees)
y-component = 3.5 m * sin(145 degrees)
Using a calculator, we find that sin(145 degrees) is approximately -0.8192.
y-component ≈ 3.5 m * (-0.8192) ≈ -2.87 m (rounded to two decimal places)
Therefore, the y-component of the vector is approximately -2.87 m.
Thus, the x-component of the vector is approximately -2.01 m, and the y-component is approximately -2.87 m.
To find the x and y components of a vector with magnitude and direction, you can use trigonometry. Let's break it down step by step:
Step 1: Determine the angle in relation to the positive x-axis.
Since the vector is 145 degrees below the x-axis, we need to find the angle between the vector and the positive x-axis. To do this, we can subtract 145 degrees from 180 degrees.
Angle = 180 degrees - 145 degrees
Angle = 35 degrees
Step 2: Calculate the x and y components.
Given the magnitude of the vector (3.5 m) and the angle in relation to the positive x-axis (35 degrees), we can use trigonometric functions to find the x and y components.
x-component = magnitude × cos(angle)
x-component = 3.5 m × cos(35 degrees)
y-component = magnitude × sin(angle)
y-component = 3.5 m × sin(35 degrees)
Now, let's calculate the x and y components:
x-component = 3.5 m × cos(35 degrees)
x-component ≈ 3.5 m × 0.8192
x-component ≈ 2.87 m
y-component = 3.5 m × sin(35 degrees)
y-component ≈ 3.5 m × 0.5736
y-component ≈ 2.01 m
Therefore, the x-component of the vector is approximately 2.87 m, and the y-component is approximately 2.01 m.