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Extra info for Applied Mathematics by Example: Exercises

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A) Calculate the speed of the moon in its orbit. (b) Assuming Newton’s law of Gravitation in the form F = GM m/r2 for the gravitational force F between two masses M and m, separated by a distance r, determine the mass of Utopia. ) 11. * A body moves at constant speed in a straight line from point A to point B in a certain time interval. 9: A body moving at constant speed in a straight line from A to B (left) and then from B to c (right). 9. After a second identical time interval it reaches point c thus sweeping out another triangle OBc.

What is their combined speed? The two trucks now impact on the third, after which all three move off together and hit the fourth, and so on. Eventually the ten trucks, coupled together, move off together down the track. What is their final speed? What is the time between the first collision and the last one? Hint: We already know the speed of the original moving truck. Work out the speed of the two coupled trucks after the first collision, and the three coupled trucks after the second collision, and look to see if there is a pattern in the numbers.

98 m/s. Use the law of conservation of momentum to calculate the speed of S after the collision. What is the coefficient of restitution in this collision? 14. Snooker ball A travelling at speed 3 m/s collides head on with an identical ball B travelling at 2m/s in the opposite direction. 8m/s and its direction of motion is reversed. Determine (a) the velocity of B after the collision, (b) the separation speed and (c) the coefficient of restitution. 15. A railway truck T1 of mass 4000 kg travelling at speed 2 m/s collides with a stationary truck T2 of mass 6000 kg.

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