What if the plane is flying towards the Southeast and wind is to the West?

plane is flying towards the Southeast with100kmph and wind is with 25 kmph to the West. find the resulting velocity of the airplane relative to the ground and direction of plane?What if the plane is flying towards the Southeast and wind is to the West?This is a vector problem.



.......................I.y

.......................I

...25...%26lt;.----------I......x

..................../.I.\

................../...I...\

................./Q..I.45\

............R./......I.......\

............../.......I.........\

............V........I...........V 100



By the use of the component method solve for the summation of forces along the Y-axis and the X-axis. Have the habit to show the forces graphically so as not to be confused in cases where you are to deal with more than two or more forces. Then solve for the Resultant:



Rx = Summation of forces along the X-axis (%26lt;-- (-) ---%26gt; + )

......= - 25 + !00(sin45)

......= -25 + 100(.707)

......= - 25 + (70.7)

Rx = 45.7 kmph E (reversed to what was assumed in diag.)



Ry = Summation of foces along the Y-axis (up+) (down -)

.....= -(100)(cos45)

....= -100(.707)

Ry = - (70.7) kmph





From Phythagorean theorem:





.......I\

.......I..\

.Ry..I....\..R

.......I.Q..\

.......I........\

......V.--------%26gt;

................Rx = 45.7 kmph





R^2 = (Ry)^2 + (Rx)^2

.......= (70.7)^2 + (45.7)^2

.......= 4998.48 + 2088.49

.......= 7086.98

...R = 84.18 kmph



Finding the direction of airplane



tan Q =Rx /Ry

..........= (45.7)/(70.7)

..........= .6464

.......Q= 32.88 degrees(S 32.88E)



Resulting Velocity of plane relative to the ground



V = 84.18 kmph directed S( 32.88 degrees)EWhat if the plane is flying towards the Southeast and wind is to the West?You have to break up the southeast vector into x- and y-components. Think of it as a 45潞 right triangle with a hypotenuse of 100 km/h.



sin(45潞)*(100) = 70.7 km/h to the South



cos(45潞)*(100) = 70.7 km/h to the East



Now you can factor in the wind. The wind is going in the opposite direction of the East component, so you subtract.



70.7 km/h - 25 km/h = 45.7 km/h



Use the Pythagorean theorem to find the resulting velocity:



(45.7)^2 + (70.7)^2 = V^2



V = 84.2 km/h



And take the inverse tangent of (-70.7 / 45.7) to find the angle. (Negative 70.7 since the direction is South.)



32.9潞 east of south



or



57.1潞 south of east

map of idaho