An 42 kmph wind blows towards 215 degrees while a plane heads towards 125 degrees at 152kmph. What is the resultant velocity of the plane? tenks vry much!!!!!!!!!!!!!!!!!!!
split the vector into components and add them up.
Or, if you're tricky, you can treat the vectors as complex numbers and wolframalpha to do the work. The only trick is remembering that complex numbers measure counterclockwise from east, while headings measure clockwise from north.
http://www.wolframalpha.com/input/?i=42+cis(90%C2%B0-215%C2%B0)+%2B+152+cis(90%C2%B0-125%C2%B0)
Then you can change that complex number back to polar coordinates, then adjust the angle to compass headings again.
I get 157.7 @ 140.5°
To find the resultant velocity of the plane, we need to use vector addition.
1. First, let's break down the wind and plane velocities into their x and y components. We can use trigonometric functions to do this.
The 42 kmph wind blows towards 215 degrees. To find the x and y components of this wind velocity, we can use the following formulas:
Wind Velocity (x-component) = Wind Speed * cos(Wind Direction)
Wind Velocity (y-component) = Wind Speed * sin(Wind Direction)
Substituting the values given:
Wind Velocity (x-component) = 42 kmph * cos(215 degrees)
Wind Velocity (y-component) = 42 kmph * sin(215 degrees)
2. Next, let's find the x and y components of the plane's velocity. The plane heads towards 125 degrees at a speed of 152 kmph.
Plane Velocity (x-component) = Plane Speed * cos(Plane Heading)
Plane Velocity (y-component) = Plane Speed * sin(Plane Heading)
Substituting the values given:
Plane Velocity (x-component) = 152 kmph * cos(125 degrees)
Plane Velocity (y-component) = 152 kmph * sin(125 degrees)
3. Now, let's add the x and y components of the wind and plane velocities to find the resultant x and y components.
Resultant Velocity (x-component) = Wind Velocity (x-component) + Plane Velocity (x-component)
Resultant Velocity (y-component) = Wind Velocity (y-component) + Plane Velocity (y-component)
4. Finally, we can use the Pythagorean theorem to find the magnitude of the resultant velocity:
Resultant Velocity = sqrt((Resultant Velocity (x-component))^2 + (Resultant Velocity (y-component))^2)
To find the direction of the resultant velocity, we can use the inverse tangent function:
Resultant Velocity Direction = atan2(Resultant Velocity (y-component), Resultant Velocity (x-component))
Now, plugging in the values and performing the calculations, we can find the resultant velocity of the plane.
To find the resultant velocity of the plane, we will use vector addition.
First, we need to convert the wind and plane velocities to their respective vector components.
The wind velocity of 42 km/h blowing towards 215 degrees can be broken down into horizontal and vertical components using trigonometry:
Horizontal component = wind speed * cos(wind direction)
Vertical component = wind speed * sin(wind direction)
Horizontal component = 42 km/h * cos(215°)
Vertical component = 42 km/h * sin(215°)
Next, we calculate the horizontal and vertical components of the plane's velocity of 152 km/h heading towards 125 degrees:
Horizontal component = plane speed * cos(plane direction)
Vertical component = plane speed * sin(plane direction)
Horizontal component = 152 km/h * cos(125°)
Vertical component = 152 km/h * sin(125°)
Now, we can add the horizontal and vertical components separately to find the resultant velocity:
Resultant horizontal component = wind horizontal component + plane horizontal component
Resultant vertical component = wind vertical component + plane vertical component
Finally, we can use the resultant horizontal and vertical components to find the magnitude and direction of the resultant velocity using Pythagoras' theorem and inverse trigonometric functions.
Resultant magnitude = sqrt(Resultant horizontal component^2 + Resultant vertical component^2)
Resultant direction = arctan(Resultant vertical component / Resultant horizontal component)
By plugging in the calculated values, you can find the resultant velocity of the plane.