(a) At 12 noon, ship A is 50 km north of ship B. 2. Ship A...

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(a) At 12 noon, ship A is 50 km north of ship B. 2. Ship A is moving west at a uniform speed of 12 km h-1. Ship B is moving in the direction west a° north at a uniform speed of 26 km h-1, 5 where sin a = 13 Express the velocities of A and B, in terms of i and 7. (i) (ii) Find the magnitude and direction of the velocity of A relative to B. (iii) Find the shortest distance between the two ships. (iv) At what time are the two ships next 50 km apart? Give your answer correct to the nearest minute. Ship P is moving north at a uniform speed of 10 km h-1. A passenger on P observes a speedboat that appears to be moving relative to P in the direction north 45° east. (b) Ship Q is moving due south at a uniform speed of 10 km h-1. A passenger on Q observes the same speedboat that appears to be moving relative to Q in the direction north 30° east. (i) Show that the speedboat is moving in the direction north 0° east, where tan 0 = 3 – 1. Hence find its speed. (ii) (a) At 12 noon, ship A is 50 km north of ship B. 2. Ship A is moving west at a uniform speed of 12 km h-1. Ship B is moving in the direction west a° north at a uniform speed of 26 km h-1, 5 where sin a = 13 Express the velocities of A and B, in terms of i and 7. (i) (ii) Find the magnitude and direction of the velocity of A relative to B. (iii) Find the shortest distance between the two ships. (iv) At what time are the two ships next 50 km apart? Give your answer correct to the nearest minute. Ship P is moving north at a uniform speed of 10 km h-1. A passenger on P observes a speedboat that appears to be moving relative to P in the direction north 45° east. (b) Ship Q is moving due south at a uniform speed of 10 km h-1. A passenger on Q observes the same speedboat that appears to be moving relative to Q in the direction north 30° east. (i) Show that the speedboat is moving in the direction north 0° east, where tan 0 = 3 – 1. Hence find its speed. (ii)

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