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Extra info for Applied Mathematics by Example: Exercises

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17. * The position vectors rA = 20i + 10j and rB = −20i + 30j represent the positions of ships A and B at time t = 0 (hours). Ship A has velocity 10j km/hr and ship B has velocity 10i + 5j km/hr. (a) Show that, at time t, rA = 20i + (10 + 10t)j, and find a similar formula for rB . (b) What are the distances between the two ships at t = 1 and t = 2? (c) Calculate the bearing of B, seen from A, at times t = 1 and t = 2. What is the evidence that the ships are on a collision course? (d) Verify that the ships will collide at t = 4.

I and j are unit vectors in the easterly and northerly directions respectively and distances are measured in kilometres). He is being carried along by an ocean current with velocity 4i, measured in km/day. Draw a sketch to represent this information. e. at t = 1)? Mr B desires to reach an island with position vector 10j. Explain why his nearest approach to the island is after 3 days. By what distance does he miss the island? The wind is coming from the south, and by hoisting a sail Mr B can change his velocity to 4i + kj, where he can choose k by varying the size of the sail.

Boy B whirls a conker in a vertical circle on a string of length 1 m. Assuming that energy is conserved during each revolution, what is the minimum speed that the conker should have at the bottom of the circle to ensure that the string remains taut when it is at the top? com 45 Click on the ad to read more Questions Applied Mathematics by Example: Exercises 5. * An aircraft flies in a parabolic path y = 5000 − 10−4 x2 , where y is height in metres and x is horizontal distance measured along the line of flight.

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