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It is known that in a vacuum the range of a projectile becomes maximum when θ0 = 45◦ . Is this still true in the presence of a fluid? 4 are needed before we can do some calculations to find an answer to this question. 4 according to a constant time increment; therefore, the range is not specifically shown in the output. Furthermore, an algorithm has to be found so that the maximum of a function can be located automatically by the computer. The range can be found approximately by using Fig. 2. Suppose that in the numerical integration the point Q is the first computed point at which the body falls back on or below the horizon.
4 reveals that the error in position is only of the order of 10−9 m and that in velocity cannot be detected when printed according to the present field specification. 3) is a function of the elevation of a projectile. If the variation is described by the curve sketched in Fig. 3, we would like to locate the angle θ0 at which the range is maximum. Let us choose an arbitrary point a on the curve and locate a second point b according to the relation (θ0 )b = (θ0 )a + δ1 where δ1 is an arbitrary incremental quantity.
5) to eliminate fi . 2). 1). 9).