Question

An airplane P is heading N 80o W at 250 m/s relative to the air. The wind blows
from N 10o E with the speed of 40 m/s relative to the ground. Find the magnitude
and direction of the velocity of airplane P relative to the ground.
In the meantime, the velocity of airplane Q relative to the air is 250 m/s in the
direction of N 20o W. What is the speed of airplane Q relative to airplane P?cannot answer !

Answer 1

First, convert the wind vector to the direction that the wind is affecting the planes. If the wind is from the Northeast, then it is blowing towards the Southwest.
Thus a 40 m/s wind from N 10 E is an 80 degree angle with respect to the positive horizontal axis. To represent the force the wind vector is 40 m/s at 260 degrees (80 + 180). This puts the vector in quadrant III.

Next calculate the resultant speed and direction with respect to the ground for Airplane P due to the influence of the wind. There are several ways this can be don. Personally, I prefer converting the vector in to its horizontal (x) and vertical (y) components.

The airplane P direction of N 80 W is at an angle of 170 degrees with the positive x axis (80+90). The x component is then 250 Cos 170 =-246.2019 the y component is 250Sin170=43.4120. The wind force vector is 40 m/s at an angle of 260 degrees with respect to the horizontal axis. Using the same method to calculate the horizontal and vertical components, I came up with : Wind: (horizontal) x=-6.9459, and vertical
y=-39.2310.

To calculate the resultant we combine the respective x components and y compoents getting an x value of -253.1478, and a y value of 4.1810 Converting back to a vector we use the pythagorean formula, inverse tan y/x getting: 253.1823 at an angle of 179.0538 degrees with respect to the positive x axis.

Do the same for Airplane Q: 250 m/s at angle 110 degrees (90+20) with respect to positive x axis. Use same values for wind as for Airplane P, converting to horizontal and vertical components as done for P & Wind force. combining we get for the resultant of Plane Q and Windforce x=(-85.5050+(-6.9459))=-92.4509 and
y=(234.9281+(-39.2310)=195.6971 Converting to a vector as for Airplane P we get a resultant of 216.2869 at an angle of 115.287 degrees with respect to the positive x axis.

Answer 2

To put the direction angles in terms of the problem: Airplane P is traveling at 253.183 m/s N 89.0538 W (almost due west). Airplane Q is traveling 216.2869 m/s N 25.287 W

Answer 3

The speed of Q relative to P. Airplane Q speed is 36.9 m/s less than P.

Answer 4

This should be big help: hyperphysics.phy-astr.gsu.edu/hbase/vect.html

Answer 5

search google for vector addition and subtraction and click on the Basic Vector Operations this was the second entry for my search.