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Additional info for Applied Mathematics by Example: Exercises
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. If he hoists the sail tomorrow, at t = 1, what is the value of k which will allow him to reach the island? What will be the total distance travelled? com 56 Questions Applied Mathematics by Example: Exercises 13. Crow C flies at a speed of 12 m/s from tree A with position vector 20i + 10j to tree B with position vector 308i + 94j. (Distances are given in metres).
A V-2 rocket of the 1939 – 1945 war had a mass of 4000 kg with a further 8000 kg of fuel. Fuel was burnt at a rate of 135 kg per second and the combustion products were ejected backwards at a speed of 2000 m/s relative to the rocket. Calculate the propulsive force exerted on the rocket. 8. 2 m. 3 m/s towards B. 2 m/s. What is the speed of A? 1 m/s. What is the speed of B? Check that the total momentum of A, B and C after both collisions have happened is still the same as their total momentum before the collisions.
5 m. e. 5 seconds when speeds of both are 11 m/s. 5 m behind. 301 s. 301 s, so A wins. 006 s × 10 m/s = 6 cm in distance. 2 Projectiles 1. 476 s. 11 m. 14 m. 23 m. 34 m and still clear net. 9/V )2 . 9/V )2 . 8 m/s. 3 m. 0 m/s. 2. (a) The bomb is released when the aeroplane is 250/ tan(10◦ ) = 1418 m short of the target. (b) The bomb takes a time (2 × 250/g) = 50/7 seconds to reach the ground, (c) during which time it travels horizontally 200×50/7 = 1429 m and so overshoots by about 11 m. 3. 7 cancels to leave quadratic 7t2 + 3t − 10 = 0, factorises to (7t + 10)(t − 1) = 0, with t = 1 second the relevant solution.