An aeroplane is moving at 200 km/h due 60.The plane experiences a wind blowing at 120 due 210.Find the resultant velocity of th
e plane by resolving the velocities into their components.
I have no idea what "due" means in this context.
I also do not know if the wind is blowing FROM 120 (navigation way) or TO 120 ( land way).
and I do not know if your angles are measured clockwise from North (navigation way) or counterclockwise from the x axis(math way)
All angles are measured CW from +y-axis.
Vr = 200km/h[60o] + 120km/h[210o].
X = 200*sin60 + 120*sin210 =
Y = 200*Cos60 + 120*Cos210 =
Vr = sqrt(X^2 + Y^2).
TanA = X/Y.
To find the resultant velocity of the plane, we need to resolve the velocities into their components.
Let's assume the direction towards 0 degrees is towards the East, and the direction towards 90 degrees is towards the North.
The plane's velocity is given as 200 km/h due 60, which means the plane is moving at 200 km/h at 60 degrees angles from the East direction.
To resolve this velocity into its components, we can use trigonometry.
The horizontal component (Vx) of the velocity can be found using the cosine function:
Vx = Velocity * cos(angle)
Vx = 200 km/h * cos(60 degrees)
Vx = 200 km/h * 0.5
Vx = 100 km/h
The vertical component (Vy) of the velocity can be found using the sine function:
Vy = Velocity * sin(angle)
Vy = 200 km/h * sin(60 degrees)
Vy = 200 km/h * √3/2
Vy = 100√3 km/h
Now, let's consider the wind velocity of 120 km/h due 210, which means the wind is blowing at 120 km/h at 210 degrees angles from the East direction.
To resolve this velocity into its components, we can again use trigonometry.
The horizontal component of the wind velocity can be found using the cosine function:
Vwx = Velocity * cos(angle)
Vwx = 120 km/h * cos(210 degrees)
Vwx = 120 km/h * (-0.5)
Vwx = -60 km/h
The vertical component of the wind velocity can be found using the sine function:
Vwy = Velocity * sin(angle)
Vwy = 120 km/h * sin(210 degrees)
Vwy = 120 km/h * (-√3/2)
Vwy = -60√3 km/h
Now, to find the resultant velocity, we need to add the corresponding components:
Resultant horizontal velocity = Vx + Vwx
Resultant vertical velocity = Vy + Vwy
Resultant horizontal velocity = 100 km/h + (-60 km/h)
Resultant horizontal velocity = 40 km/h
Resultant vertical velocity = 100√3 km/h + (-60√3 km/h)
Resultant vertical velocity = 40√3 km/h
Using the Pythagorean theorem, we can find the magnitude of the resultant velocity:
Resultant velocity = √((Resultant horizontal velocity)^2 + (Resultant vertical velocity)^2)
Resultant velocity = √((40 km/h)^2 + (40√3 km/h)^2)
Resultant velocity ≈ √(1600 km^2/h^2 + 2400 km^2/h^2)
Resultant velocity ≈ √4000 km^2/h^2
Resultant velocity ≈ 63.24 km/h
Therefore, the resultant velocity of the plane, when considering both its initial velocity and the wind velocity, is approximately 63.24 km/h.
To find the resultant velocity of the plane, we need to resolve both the plane's velocity and the wind's velocity into their respective components. Let's break down the problem step by step:
1. Start by breaking down the plane's velocity into its horizontal and vertical components. We have the following information:
- The plane is moving at 200 km/h due 60 (that means the direction of the velocity is 60 degrees with respect to the horizontal axis).
To find the horizontal component (Vx) of the plane's velocity, we can use trigonometry:
Vx = Velocity * cos(Angle)
Vx = 200 km/h * cos(60 degrees)
Vx = 100 km/h
To find the vertical component (Vy) of the plane's velocity:
Vy = Velocity * sin(Angle)
Vy = 200 km/h * sin(60 degrees)
Vy = 173.2 km/h
So, the plane's velocity components are:
Vx = 100 km/h horizontally
Vy = 173.2 km/h vertically
2. Next, let's resolve the wind's velocity into its horizontal and vertical components. We have the following information:
- The wind is blowing at 120 km/h due 210 (that means the direction of the wind's velocity is 210 degrees with respect to the horizontal axis).
To find the horizontal component (Wx) of the wind's velocity:
Wx = Velocity * cos(Angle)
Wx = 120 km/h * cos(210 degrees)
Wx ≈ -103.9 km/h
To find the vertical component (Wy) of the wind's velocity:
Wy = Velocity * sin(Angle)
Wy = 120 km/h * sin(210 degrees)
Wy ≈ -91.2 km/h
So, the wind's velocity components are:
Wx ≈ -103.9 km/h horizontally
Wy ≈ -91.2 km/h vertically
3. Now, to find the resultant velocity, we simply add the respective components together:
Resultant horizontal velocity (Rx) = Vx + Wx
Rx = 100 km/h + (-103.9 km/h)
Rx ≈ -3.9 km/h
Resultant vertical velocity (Ry) = Vy + Wy
Ry = 173.2 km/h + (-91.2 km/h)
Ry = 82 km/h
So, the resultant velocity of the plane is approximately:
Rx ≈ -3.9 km/h horizontally
Ry = 82 km/h vertically