the navigator of an airplane plans a flight 1200 km away, in a direction 30degrees E of N. he is informed of a prevailing wind from the west of 80 km/h. the pilot wants to maintain an air speed of 300km/h.
a) what heading should the navigator give the pilot?
the answer is 17degrees E of N
b) how long will the flight take?
the answer is 3.6 hours
c) how much time did the wind save?
the ans is 0.41 hours
thanks!!!
2007-02-25 02:51:15 · 1 answers · asked by Anonymous in Science & Mathematics ➔ Physics
I'm not quite getting these exact numbers but here are my calculations.
30 degrees e of north is 60 degrees off of the x axis of travel
the heading needs to be changed so that the 80 km/hr wind is canceled out by t he direction while maintaining the airspeed of 300
so cos(A)=80/300 ==> A=74.5 degrees but to get back to the problem's notation, subtract it from 90 degrees to get 15.5 degrees
the vector velocity with the wind is
(300cos(60) +80) i + 300sin(60) j. the magnitude of this velocity is sqrt(230^2+(259.8)^20 = 347 km/hr
time of travel is 1200/347 =3.5 hrs
the time of travel without the wind would be 1200/300 or 4 hrs so the wind saved 0.5 hrs.
2007-02-25 05:00:10 · answer #1 · answered by Rob M 4 · 1⤊ 0⤋