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A remote-controlled model aeroplane has a speed in still air of 4.2m s^-1. It is pointed in the direction N 82 degrees W but flies in a wind of speed 9.1ms^-1 from the direction N 39 degrees E. Take i to be 1 m s^-1 due east and j to be


1ms^-1 due north





Q The aeroplane starts from a point on the east boundary of a rectangular park whose east and west boundaries run due north-south and are 420m apart. Find the time taken for the aeroplane to cross the park to the west boundary and the distance north or south that it has then travelled|||Are you sure that you have the speeds right? The idea would be to combine the plane's velocity in still air plus the wind velocity to get a resultant velocity, then use this resultant velocity to work out time taken and "drift" north.





In terms of unit velocity vectors i and j the plane's velocity is


4.2 cos(8 degrees) i + 4.2 sin(8 degrees) j


if I'm interpreting the direction N 82 degrees W correctly!





Similarly the wind velocity is


-9.1 cos(51 degrees) i + 9.1 sin(51 degrees) j


again assuming the direction N 39 degrees E is interpreted correctly.





So the plane's resultant velocity is


[4.2 cos(8 degrees) - 9.1 cos(51 degrees)] i


+ [4.2 sin(8 degrees) + 9.1 sin(51 degrees)] j


= -1.56 i + 7.65 j





This is why I asked whether your velocities are right since the plane is actually travelling eastward! But the principle will be the same and you can plug in different velocities to get the correct answer.