Question

The good ship Beegull is travelling in perfectly calm seas on course for a small remote island, to carry out a wildlife survey. It is travelling at a speed (relative to the surrounding sea) of 40 km h−1 with a bearing of 55◦ . It is initially on course to enter harbour at the island assuming no change in the sea conditions. Unfortunately, unknown to the crew, a strong current arises of 15 km h−1 in the direction from north-west to south-east. Take unit vectors i to point east and j to point north. (a) Express the original velocity v of the ship relative to the sea and the velocity c of the current in component form, giving numerical values in km h−1 to one decimal place. (b) Express the resultant velocity w of the ship in component form, giving numerical values in km h−1 to one decimal place. (c) Hence find the magnitude and direction of the resultant velocity w of the ship, giving the magnitude in km h−1 to one decimal place and the direction as a bearing to the nearest degree. (d) If the ship was 100 km from the island harbour when the current arose, what will be the shortest distance between the ship and the harbour when it misses the harbour because of the current? Give your answer to the nearest km. You may find it helpful to draw a diagram. You can assume there is no other land in the vicinity.

Answer 1