1)The x- and y-components of a velocity vector of 100 N at 240 degrees would be?
2) A man pushes a lawn mower across the lawn exerting 5 N of force along the handle at an angle of 25 degrees with the ground. What is the x-component of the force he exerts?
1) The answer depends upon what reference direction the 240 degrees is measured from, and whether + means couterclockwise or counterclowise. In mathematics and physics, polar direction angles are measured counterclockwise from +x. I assume you are dealing with a Force (F) vector and that is how the angle is measured.
Then the vector is in the third quadrant and
Fx = 100N cos 240 = -100N cos 60 = -50N
Fy = 100N sin 240 = -100N sin 60 = ?
2) 5N cos 25
1) To find the x- and y-components of a velocity vector at a given angle, you can use trigonometry.
First, we need to find the magnitude of the x- and y-components. The magnitude of an x-component can be determined by multiplying the magnitude of the vector with the cosine of the angle, while the magnitude of the y-component can be determined by multiplying the magnitude of the vector with the sine of the angle.
In this case, the magnitude of the velocity vector is 100 N and the angle is 240 degrees.
The x-component can be calculated as: x = magnitude * cosine(angle)
x = 100 N * cos(240 degrees)
Similarly, the y-component can be calculated as: y = magnitude * sine(angle)
y = 100 N * sin(240 degrees)
To perform these calculations, make sure to use the appropriate trigonometric functions on your calculator, set in degrees mode.
2) In this problem, we have a force applied at an angle with respect to the ground. We are interested in finding the x-component of this force, which represents the force acting horizontally.
To calculate the x-component of the force, we can use trigonometry. The x-component can be found by multiplying the magnitude of the force by the cosine of the angle.
In this case, the magnitude of the force is 5 N and the angle with the ground is 25 degrees.
The x-component can be calculated as: x = magnitude * cosine(angle)
x = 5 N * cos(25 degrees)
Make sure to use the appropriate trigonometric function for cosine on your calculator, set in degrees mode, to find the answer.