Question

An airplane P is heading N 80 W at 250 m/s relative to the air. The wind blows
from N 10 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 20 W. What is the speed of airplane Q relative to airplane P?

Answer 1

thanks,i want to know how's the diagram of the 2nd question,the new relative velocity of airplane q is affected by the new relative velocity of airplane p,how is it so??

Answer 2

Q by wind =285.34

Answer 3

then??

Answer 4

okay,its already midnight here,see you later

Answer 5

I have made too many errors I have deleted my responses. I did however, agree with the 285.34 resultant. I am going to regroup and try later.

Answer 6

The angle between vectors P and W is 90, so magnitude of resultant vector is hypotenuse of right triangle
--> x^2 = 250^2 + 40^2 --> x = 253.18 m/s
Direction can be found by using trig
let angle between P and resultant vector be A
sinA = 40/253.18 --> A = 9.09
so new direction is N 89.09 W


The angle between vectors Q and W is 150, find magnitude of resultant vector using law of cosines
--> x^2 = 250^2 +40^2 -2(250)(40)cos(150)
--> x = 285.34 m/s
Direction can be found by using law of sines
let angle between Q and resultant vector be A
sinA/40 = sin(150)/285.34 --> A = 4.02
so new direction is N 24.02 W

P' and Q' will denote resultant vectors

the magnitude of the resultant vector of P' and Q' is speed of Q relative to P
The angle is 65.07 between them, so using law of cosines
x^2 = 253.18^2 + 285.34^2 -2(253.18)(285.34)cos(65.07)
--> x = 290.89 m/s