If vertical component of a vector is equal to its horizontal component , the angle made by the vector with x axis?
To find the angle made by a vector with the x-axis when its vertical component is equal to its horizontal component, you can use trigonometry.
Let's assume the vertical component and horizontal component of the vector are both equal to "v".
The magnitude of the vector can be found using the Pythagorean theorem:
Magnitude (m) = sqrt(vertical component^2 + horizontal component^2)
= sqrt(v^2 + v^2)
= sqrt(2v^2)
= sqrt(2) * v
Since the vertical component and horizontal component are equal, you can rewrite the magnitude as:
Magnitude (m) = sqrt(2) * v
Now, let's consider the right triangle formed by the vector, the x-axis, and a vertical line connecting the vector to the x-axis. The angle between the vector and the x-axis (θ) can be defined as:
tan(θ) = (vertical component) / (horizontal component)
Since the vertical and horizontal components are equal, you can simplify it to:
tan(θ) = v / v
= 1
Inverse tangent (atan) is the function used to find the angle from a ratio:
θ = atan(tan(θ))
= atan(1)
Therefore, the angle made by the vector with the x-axis is:
θ = atan(1)
Using a scientific calculator or programming, you can find the inverse tangent of 1. This angle will depend on your calculator settings (degrees or radians). So, make sure to set it appropriately.
If your calculator is in degrees mode, the angle will be:
θ ≈ 45 degrees
If your calculator is in radians mode, the angle will be:
θ ≈ π/4 radians
Hence, the angle made by the vector with the x-axis when its vertical component is equal to its horizontal component is approximately 45 degrees or π/4 radians.
If the vertical component of a vector is equal to its horizontal component, it implies that the vector forms a right-angled triangle with the x-axis. In such a case, the angle made by the vector with the x-axis is 45 degrees or π/4 radians. This is because in a right-angled triangle, the two sides (horizontal and vertical components in this case) are equal when the triangle is an isosceles right-angled triangle.
Given that vertical component = Horizontal component
Therefore Tanθ = 1
Tanθ is 1 when θ=45°
Therefore Angle made by vector with x-axis is 45°