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**Extra resources for Applied Mathematics by Example - Exercises**

**Example text**

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. 12. * Snooker player P is attempting to pot ball B. If he is to be successful, ball B must move off at an angle of 45◦ after being struck by the cue ball A. This in turn requires that at the moment of impact the centres of the two balls must be in alignment with the pocket, so that cue ball A must travel in the direction AA1 (see diagram).

What point is this? (f ) Calculate the ratios of the lengths AG : AD, BG : BE, CG : CF. 4. ABCD is a parallelogram with DC parallel to AB and AD parallel to BC. The position vectors of its corners are a, b, c, and d respectively. (a) Calculate d in terms of a, b, and c. (b) Find the position vector M of the mid-point of the diagonal AC. (c) Show that M also lies on the other diagonal BD and divides it into two equal parts BM and MD. com 54 Questions Applied Mathematics by Example: Exercises 5. ABCD is a parallelogram with DC parallel to AB and AD parallel to BC.

1 mph. Speed limit broken. 5. Quadratic equation is 5000 = 300t+t2 . 83 seconds. 6. , gives s = 51 m. (b) If the stone is thrown at 15 m/s upwards, instead of downwards, then the same method applies but with u = −15, and since (−15)2 = (+15)2 , the solution is the same, s = 51 m. Alternatively, it is valid to split the flight of the stone into two parts, upwards and downwards, and combine the results, but this is more laborious than is really necessary. Let the equations do the work! 7. 5 m respectively.