An airplane flies at 65 m/s in the direction 149 degrees counter clockwise from east. What are the east and north components of the plane's velocity?

Vector = 65m/s @ 149 deg.

X = hor = 65*cos149 = -55.72m/s = East.

Y = ver = 65*sin149 = 33.48m/s = North Comp.

Well, I hope the airplane remembered to bring its compass! To find the east and north components of the velocity, we can use a bit of trigonometry.

First, we need to find the east component of the velocity. Since the plane is flying at an angle of 149 degrees counter clockwise from east, that means it's 41 degrees clockwise from north. So the east component can be found by multiplying the velocity (65 m/s) by the cosine of 41 degrees. Let me calculate that for you...

*Clown Bot puts on a tiny lab coat and starts scribbling on a tiny chalkboard*

Cos(41 degrees) ≈ 0.759

65 m/s * 0.759 ≈ 49.33 m/s

Therefore, the east component of the plane's velocity is approximately 49.33 m/s.

Now, to calculate the north component, we multiply the velocity (65 m/s) by the sine of 41 degrees.

Sin(41 degrees) ≈ 0.649

65 m/s * 0.649 ≈ 42.19 m/s

So, the north component of the plane's velocity is approximately 42.19 m/s.

So, the east component is approximately 49.33 m/s, and the north component is approximately 42.19 m/s. Good luck catching up with those good north vibes!

To find the east and north components of the plane's velocity, we will use trigonometry.

Let's break down the given information:

- The plane is flying at a speed of 65 m/s.
- The direction is 149 degrees counter clockwise from east.

First, let's determine the east component. To do this, we use the cosine function:

East component = Velocity * cos(direction)

East component = 65 m/s * cos(149 degrees)

Now, let's calculate the north component. To find this, we use the sine function:

North component = Velocity * sin(direction)

North component = 65 m/s * sin(149 degrees)

Calculating each component:

East component = 65 m/s * cos(149 degrees)
East component ≈ -33.92 m/s (rounded to two decimal places)

North component = 65 m/s * sin(149 degrees)
North component ≈ 56.48 m/s (rounded to two decimal places)

Therefore, the east component of the plane's velocity is approximately -33.92 m/s, and the north component is approximately 56.48 m/s.

To find the east and north components of the plane's velocity, we can break down the given velocity vector into its horizontal (east) and vertical (north) components.

First, let's convert the given direction of 149 degrees into a standard unit circle reference angle. Since the direction is counter-clockwise from east, we can subtract 90 degrees from it to get the reference angle.

149 degrees - 90 degrees = 59 degrees

Now, we can use trigonometry to find the east and north components of the velocity. The east component (V_east) can be found using the cosine function, and the north component (V_north) can be found using the sine function.

V_east = velocity * cos(reference angle)
= 65 m/s * cos(59 degrees)
≈ 31.68 m/s

V_north = velocity * sin(reference angle)
= 65 m/s * sin(59 degrees)
≈ 55.04 m/s

Therefore, the east component of the plane's velocity is approximately 31.68 m/s, and the north component is approximately 55.04 m/s.