A heir walus 14.7km of angle of 35°East of North the west on north component of this work
If V×=9.8mls and V× detrimine the mangtuid and direction
To find the magnitude and direction of the west component of the velocity vector V:
Given:
Angle of 35° east of north
Magnitude of Vx = 9.8 m/s
First, we need to determine the north component of V.
Using trigonometry, we can find the north component (Vn) by using the angle and the magnitude:
Vn = V × sin(35°)
Vn = 9.8 m/s × sin(35°)
Vn ≈ 5.707 m/s (rounded to 3 decimal places)
Next, we can determine the west component (Vw) using the north component (Vn) and the angle:
Vw = Vn × cos(35°)
Vw = 5.707 m/s × cos(35°)
Vw ≈ 4.662 m/s (rounded to 3 decimal places)
Therefore, the magnitude of the west component (Vw) is approximately 4.662 m/s.
To find the direction, we need to determine the angle of the direction from the positive x-axis (east).
Using trigonometry, we can find the angle (θ) by using the north and west components:
tan(θ) = Vw / Vn
θ = arctan(Vw / Vn)
θ = arctan(4.662 m/s / 5.707 m/s)
θ ≈ 39.76° (rounded to 2 decimal places)
The direction of the west component of the velocity vector V is approximately 39.76° east of north.