Vector............?

An airplane flies from San Francisco to Washington Dc at a speed of 8000km/hr. Assume Washington is due east of San Francisco at a distance of 6000km. Use a Cartesian system of coordinates centered at San francisco with Washington in the positive x- direction. At cruising altitude, there is a cross wind blowing from north to south of 100km/hr.





A)What must be the direction of flight for the plane to actually arrive in Washington?





B)what is the speed in the San Francisco to Washington direction?





C) How long does it take to cover this distance?





D) What is the time difference compared to no crosswind?|||First of all...8000km/hr is a very fast airplane...are you sure that is correct?


If it is...then..for every 8000 km it travels in the x direction, it is pushed by the crosswind 100 km.


Therefore, for every 80 km in the x direction, it is 1 km in the y.


Dividing that into 6000 km, the plane is pushed 75 km south during the entire trip.


The plane therefore needs to aim for 75 km north of DC to reach it.


At this point, it is useful to point out that the new distance [sqrt(6000^2+75^2)] is just over 6000, so the negligable extra amount the plane must travel will not affect the answer by more than maybe a couple tenths.


Solving the triangle, we find that the plane must aim an extra 0.7161599454704084 degrees in the north direction so that the wind will blow it perfectly to DC.


For part B, if it is traveling 8000 km/hr in the barely north and mostly east direction, then, solving the vector triangle, it is traveling 7999.375073232652 km/hr in the east directoin


For the plane to cover the 6000.4ish km/hr distance at 8000 km/hr pace, it will take a very small fraction of a second over 45 seconds.


Therefore, for part D, the difference is a very small fraction of a second...If you need the actual answer for that...you should find someone with more time on their hands to figure it all out perfectly :)


Hope this helps. And i hope its correct