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4. A particle of mass m moves vertically under gravity in a medium which offers a resistance proportional to the square of the speed.

4. A particle of mass m moves vertically under gravity in a medium which offers a resistance proportional to the square of the speed. The terminal speed of fall is U. The particle is projected upwards with speed U. Show that the greatest height attained is (U2/2g) log 10 and find the speed with which it returns to the point of projection. 9

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