a plane has an airspeed of 200 mph. the pilot wants to reach a destination 600 miles east but a wind is blowing 50 mph 30 degrees North of East. What direction must the pilot head the plane in order to reach the destination?
I asked my Lab T.A. and she helped me understand that I basically need to draw two vectors and get the average of the two but all of my answers are wrong so far...
Not the average of the two - you need to find the vector which, when added to the windspeed vector, will give the vector to the desired destination. So you are really subtracting vectors. Try that....
It's still confusing me...200mph-50 gives us 150mph but how do i know the angle of that vector? I know it's South of East...
nevermind! got it! thanks!
way to be persistent! now you probably won't forget how it's done, since you worked so hard.
To determine the direction the pilot should head the plane, you need to consider the vector sum of the plane's airspeed and the wind's velocity. Here's how you can calculate it step by step:
1. Start by drawing a diagram to represent the situation. Draw an arrow to represent the plane's airspeed of 200 mph pointing east, and another arrow to represent the wind's velocity of 50 mph, 30 degrees North of East. Make sure to label the vectors and indicate their magnitudes and directions.
2. Break down each vector into its horizontal (east/west) and vertical (north/south) components. Since the plane's airspeed is entirely in the east direction, its horizontal component is 200 mph, and its vertical component is 0 mph. For the wind's velocity, its horizontal component can be found by multiplying its magnitude (50 mph) by the cosine of the angle, and the vertical component by multiplying its magnitude by the sine of the angle.
Horizontal component of wind velocity = 50 mph * cos(30 degrees)
Vertical component of wind velocity = 50 mph * sin(30 degrees)
Calculate these values using a calculator to get the specific values.
3. Add the horizontal components of the plane's airspeed and wind's velocity together. This will give you the resultant horizontal component:
Resultant horizontal component = Plane's airspeed horizontal component + Wind's velocity horizontal component
4. Add the vertical components of the plane's airspeed and wind's velocity together. This will give you the resultant vertical component:
Resultant vertical component = Plane's airspeed vertical component + Wind's velocity vertical component
5. Use the resultant horizontal and vertical components to calculate the magnitude and direction of the resultant vector. The magnitude can be found using the Pythagorean theorem:
Magnitude of the resultant vector = √[(Resultant horizontal component)^2 + (Resultant vertical component)^2]
The direction can be found using trigonometry:
Direction of the resultant vector = atan2(Resultant vertical component, Resultant horizontal component)
6. The direction you obtained in step 5 represents the direction the pilot should head the plane in order to reach the destination. Remember to reference this direction relative to the initial east direction.
Following these steps should help you determine the correct direction for the pilot to head the plane.