A bird has a flight speed in still air of 9.1 m s−1. It is pointed in the direction N33◦E, but flies in a wind of speed 14.8 m s−1 from the direction S 70◦E. Take i to be 1 m s−1 due east and j to be 1 m s−1 due north. Also, take vb to be the velocity of the bird in still air, vw to be the velocity of the wind, v to be the resultant velocity of the bird.
(a) Express each of the vectors vb and vw in component form, giving the components correct to 4 decimal places.
(b) Find the overall speed |v| of the bird (to 4 significant figures), and its direction of travel as a bearing (with the angle correct to 1 decimal place).
(c) The bird begins its flight from a point on the south bank of a river that flows due west and is 270 metres wide. How long does it take the bird to cross the river, and what is the distance that it has travelled in this time? Give your answers to 3 significant figures.