Mathematical questions and solutions in continuation of the mathematical columns of "the Educational times" Volume 63

 
9781153578875: Mathematical questions and solutions in continuation of the mathematical columns of

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1895 edition. Excerpt: ...the force of gravity? Solution by Beatrice A. Ward, B.sc; Professor Chakrivarti; and others. Height of plane is 300 ft.; hence the time taken to fall the height = f A/3 sees. The weight would describe space equal to height (300 ft.) in time taken to fall the height (J-v3 sees.), if initial velocity, when it commences to describe the space, is equal to 16 A/3 ft. per sec. (Given by equation = ut + t2g sin 9.) And distance (D) from top of plane in which this velocity would be acquired is 20 ft. Hence the required distance is 20 ft. 12537. (Professor Orchard, B.sc, M.A.)--The elliptic lamina Ix1 + 9jr = 28 has two equal particles placed at the ends of its minor axis, and the tangent and normal at any point are the principal axes there. Show that the mass of each particle is one-fourth that of the disc. Solution by Rev. D. T. Griffiths, M.A.; Prof. Sabkar; and others. The tangent and normal at any point are the principal axes there, provided foci of inertia coincide with foci of ellipse. Required condition, adopting usual notation, at-(A-B)/(M + 2m)i, A = iM42 + 2mi2, B = Jmj2;.-. m/M = f.e3/(l-22). This is the solution of an example given in Routh's "Rigid Dynamics." For the particular case in question, put e2 = $, and we have m = JM. 12510. (Professor Hudson, M.A.)--When wheat is Is. a bushel, bread is Jd. a lb. What should the 4-lb. loaf cost when wheat is 28s. a quarter? Solution by T. Savage; B. T. Brierley; and others. At 8s. a quarter, the 4 lbs. cost Id., hence required price is 3Jd. 12577. (Professor Finkel.)--Between Sing-Sing and Tarry-Town, I met my worthy friend, John Brown, And seven daughters, riding nags, and every one had seven bags; In every bag were thirty cats, and every cat had forty rats, Besides a brood...

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