An airplane is flying horizontally at 115 m/s, at a 20.5 degree angle north of east. State its velocity in rectangular coordinates. Assume that north and east are in the positive direction.
sin 20.5 = 0.35
cos 20.5 = 0.94
so its velocity = 115*.94i + 115*.35j
= ...
148
To find the velocity of the airplane in rectangular coordinates, we need to break down its velocity into its eastward (x-component) and northward (y-component) components.
Given:
Magnitude of velocity (v): 115 m/s
Angle (θ): 20.5 degrees north of east
To find the x-component (Vx) and y-component (Vy) of the velocity, we can use trigonometry.
Step 1: Find the x-component (Vx):
Vx = v * cos(θ)
Substituting the given values:
Vx = 115 m/s * cos(20.5°)
Using a calculator, we find:
Vx ≈ 108.7 m/s (rounded to one decimal place)
Step 2: Find the y-component (Vy):
Vy = v * sin(θ)
Substituting the given values:
Vy = 115 m/s * sin(20.5°)
Using a calculator, we find:
Vy ≈ 39.7 m/s (rounded to one decimal place)
Therefore, the velocity of the airplane in rectangular coordinates is approximately:
Vx ≈ 108.7 m/s (eastward)
Vy ≈ 39.7 m/s (northward)