An aeroplane flies horizontally at 80m/s in still air. If the aviator wishes to fly due south and the wind is blowing from south-east at 30m/s.(1) what course must he steer?(2)how long will it take him to arrive at his destination 200km away?
3 answers
What direction is the plane flying? It makes a difference in the final velocity.
Actually, I was wrong. You want two vectors
v + w = <0,-y>
where y is the final speed of the plane.
If v is the velocity of the plane, then v = <x,√(80^2-x^2)>
and w is the wind's velocity, which is <21.2,-21.2>
So now, add up the x- and y-components and solve for the values to use.
v + w = <0,-y>
where y is the final speed of the plane.
If v is the velocity of the plane, then v = <x,√(80^2-x^2)>
and w is the wind's velocity, which is <21.2,-21.2>
So now, add up the x- and y-components and solve for the values to use.
1. Vp + Vw = -80i
Vp + 30[135o] = -80i,
Vp -21.2 + 21.2i = -80i,
Vp = 21.2 - 101.2i = 103.4m/s[-78.2o].
Direction = 78.2 degrees S. of E. = 11.8o E. of S.
2. V*T = 200,000 m.
80T = 200,000 ,
T = 2500 s. = 41.7 min.
Vp + 30[135o] = -80i,
Vp -21.2 + 21.2i = -80i,
Vp = 21.2 - 101.2i = 103.4m/s[-78.2o].
Direction = 78.2 degrees S. of E. = 11.8o E. of S.
2. V*T = 200,000 m.
80T = 200,000 ,
T = 2500 s. = 41.7 min.
3 answers