Question

Physics Hang Glider

You are flying a hang glider at 14 mph in the northeast direction (45°). The wind is blowing at 4 mph from due north.

a) What is your airspeed?

b) What angle (direction) are you flying?

c) The wind increases to 14 mph from the north. Now what is your airspeed and what direction are you flying? If your destination is to the northeast, how would you change your speed or direction so you might make it there? Test your answer using the sim.

Answer 1

Given

you are flying with 14 mph noreast direction (45°)

wind is blowing at 4 mph from due north.(that is to South)

let +X axis as reference axis

the writing the components of the velocity of you and wind as

let

you is Y = Yx i + Yy j

Y = 14 cos 45 i + 14 sin45 j

Y = 9.9 i + 9.9 j

wind is to the south so it has only y component that is  

W = Wx i + Wy j

W = 4 cos 270 i + 4 sin270 j

W = 0 i - 4 j

NOW resultant is  

R = Rx i + Ry j

R = (9.9+0)i +(9.9-4) j

R = 9.9 i + 5.9 j

the magnitude is R = sqrt(9.9^2+5.9^2) mph = 11.524 mph

the direction is tan theta = (5.9/9.9) ===> theta = arc tan (5.9/9.9) = 30.8 degrees

a) your airspeed is 11.524 mph

b) the direction is 30.8 degrees

c) if the wind speed become 14 mph then  

W = 14 cos 270 i + 14 sin270 j

W = 0 i - 14 j

resultant is  

R = Rx i + Ry j

R = (9.9+0)i +(9.9-14) j

R = 9.9 i - 4.1 j

the magnitude is R = sqrt(9.9^2+(-4.1)^2) mph = 10.715 mph

the direction is tan theta = (-4.1/9.9) ===> theta = arc tan (-4.1/9.9) = -22.5 degrees

the direction of you will be changed

to move northeast direction , the speed of you should be greater than the wind always.