I have had problems answering the following question, I seem to come to the "correct numbers" in part a, but the number appears to belong to the wrong component or is +ve rather than -ve or vice versa. Please could someone Help me with this, and explain how the answers are come by? Even if you can show me how to do part a) and where I might be going wrong would be great.
(b), (c), (d), require non rounded answers from previous parts in their calculations to prevent rounding errors.
An aeroplane has a cruising speed in still air of 250ms -1. It is pointed in the direction of N72 oW, but files in a wind speed of 12.8ms -1 FROM the direction N14 oE. Take i to be 1ms -1 due east and j to be 1ms -1 due north. Also, take
v a to be the velocity of the aeroplane in still air,
v w to be the velocity of the wind,
v to be the resultant velocity of the aeroplane.
a) Express each of the vectors v a and v w in component form, giving the components to 4 decimal places.
b) Hence show that the resultant velocity v of the aeroplane is given in component form approximately by
v=-240.8607 i+64.8345 j
c) Find the overall speed | v| of the aeroplane (in ms -1 to 1 decimal place) and its direction of travel, as a bearing (with the angle in degrees to 1 decimal place).
d) How long does it take the aeroplane to travel 100km? How far west does it travel in this time? Give your answer in seconds and kilometres, respectively, to 3 significant figures.
