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# A projectile is fired from the origin with angle of ISBN: 9781285740621 127

## Solution for problem 3 Chapter 13

Calculus | 8th Edition

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Problem 3

A projectile is fired from the origin with angle of elevation and initial speed v0. Assuming that air resistance is negligible and that the only force acting on the projectile is gravity, t, we showed in Example 13.4.5 that the position vector of the projectile is rstd sv0 cos dt i 1 fsv0 sin dt 2 1 2 tt 2 g j We also showed that the maximum horizontal distance of the projectile is achieved when 45 and in this case the range is R v 2 0yt. (a) At what angle should the projectile be fired to achieve maximum height and what is the maximum height? (b) Fix the initial speed v0 and consider the parabola x 2 1 2Ry 2 R2 0, whose graph is shown in the figure at the left. Show that the projectile can hit any target inside or on the boundary of the region bounded by the parabola and the x-axis, and that it cant hit any target outside this region.(c) Suppose that the gun is elevated to an angle of inclination in order to aim at a target that is suspended at a height h directly over a point D units downrange (see the figure below). The target is released at the instant the gun is fired. Show that the projectile always hits the target, regardless of the value v0, provided the projectile does not hit the ground before D. _R 0 R 0 D y x y x

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##### ISBN: 9781285740621

Since the solution to 3 from 13 chapter was answered, more than 251 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Calculus, edition: 8. This full solution covers the following key subjects: projectile, target, height, fired, HIT. This expansive textbook survival guide covers 16 chapters, and 250 solutions. The full step-by-step solution to problem: 3 from chapter: 13 was answered by , our top Calculus solution expert on 11/10/17, 05:27PM. Calculus was written by and is associated to the ISBN: 9781285740621. The answer to “A projectile is fired from the origin with angle of elevation and initial speed v0. Assuming that air resistance is negligible and that the only force acting on the projectile is gravity, t, we showed in Example 13.4.5 that the position vector of the projectile is rstd sv0 cos dt i 1 fsv0 sin dt 2 1 2 tt 2 g j We also showed that the maximum horizontal distance of the projectile is achieved when 45 and in this case the range is R v 2 0yt. (a) At what angle should the projectile be fired to achieve maximum height and what is the maximum height? (b) Fix the initial speed v0 and consider the parabola x 2 1 2Ry 2 R2 0, whose graph is shown in the figure at the left. Show that the projectile can hit any target inside or on the boundary of the region bounded by the parabola and the x-axis, and that it cant hit any target outside this region.(c) Suppose that the gun is elevated to an angle of inclination in order to aim at a target that is suspended at a height h directly over a point D units downrange (see the figure below). The target is released at the instant the gun is fired. Show that the projectile always hits the target, regardless of the value v0, provided the projectile does not hit the ground before D. _R 0 R 0 D y x y x” is broken down into a number of easy to follow steps, and 246 words.

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