By J. Pickles

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C) Using Kepler’s third law, calculate the radius of Pluto’s orbit around the Sun, assuming it to be a circle (radius of Earth’s orbit is 150 million km). Sometime later it was discovered that Pluto has a moon (called Charon). 0003 degrees. ) The time for Charon to complete one revolution in its orbit around Pluto is 6 12 days. Estimate: (d) the radius of Charon’s orbit around Pluto, and (e) the mass of Pluto. 6. 35 × 1022 kg respectively, and the distance between their centres as 384,400 km, calculate the position of the centre of gravity of the combined Earth-Moon system.

Com 57 Questions Applied Mathematics by Example: Exercises 16. Mr B is out for a walk with his dog F. Starting from the entrance to the park at E, with position vector rE = 2j, Mr B walks with speed 1 metre per second towards the point X with position vector rX = 20i + 17j. (a) Calculate the distance EX. (b) Deduce the time taken for Mr B to reach X. On entering the park F immediately darts off at constant speed to investigate a bush at Y, with position vector rY = −16i+65j. He inspects the bush for 5 seconds before dashing back on a straight line course (at the same constant speed) to intercept Mr B at X.

O is at the top of a tall tree OG and M is, initially, at the top of another tall tree of equal height, the two trees being a distance L apart. M now jumps from his tree and, holding the string, falls in a circular arc with centre O. If the angle between OA and the vertical is θ, express in terms of θ: (a) the speed of the monkey, and (b) the tension in the string. The string breaks when the tension in it exceeds 12 mg. Show that at this instant 5 θ = arcsin(3/5). Show also that M hits the trunk of tree OG after a further time 3 8 5L .

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