Find the components of vector u with a magnitude of 10 and a direction angle of ∅=54°
Help??
horizontal (x) component
... magnitude * cosine
vertical (y) component
... magnitude * sine
Thank you
Sure! To find the components of vector u with a magnitude of 10 and a direction angle of ∅=54°, we can use trigonometry.
First, let's understand what the direction angle (∅) means. The direction angle (∅) is the angle between the positive x-axis and the vector.
In this case, the direction angle (∅) is given as ∅=54°.
To find the component of vector u along the x-axis (uₓ), we can use the cosine function:
uₓ = magnitude of u * cos(∅)
uₓ = 10 * cos(54°)
To find the component of vector u along the y-axis (uᵧ), we can use the sine function:
uᵧ = magnitude of u * sin(∅)
uᵧ = 10 * sin(54°)
Now, let's calculate these values:
uₓ = 10 * cos(54°) ≈ 5.82
uᵧ = 10 * sin(54°) ≈ 8.08
Therefore, the components of vector u with a magnitude of 10 and a direction angle of ∅=54° are uₓ ≈ 5.82 and uᵧ ≈ 8.08.
I hope this helps!