Projectile Motion Problem: Sir Francis Drakes ship fires a cannonball at an enemy

Chapter 13, Problem 3

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Projectile Motion Problem: Sir Francis Drakes ship fires a cannonball at an enemy galleon. At time t = 0 seconds the cannonball has an initial velocity of 200 ft/sec and a 20 angle of elevation (Figure 13-5h). You are to find the cannonballs position P(x, y) as a function of time. Assume the point (0, 10) represents the point from which the cannonball was fired. Figure 13-5h a. Find parametric equations of the cannonballs path. To do this, assume there is no air friction, so the horizontal velocity remains what it was at time t = 0. The vertical velocity is what it was at t = 0, minus 16t 2 due to the action of gravity. Also, recall that distance = (rate)(time). b. Plot the parametric equations. Use a window for x large enough to show the point where the cannonball hits the water. Sketch the result. c. The galleon is at x = 900 ft from Sir Francis ship. The tops of the sails are 40 ft above the surface of the water. Will the cannonball fall short of the galleon, pass over the galleon, or hit it somewhere between the waterline and the tops of the sails? Show how you get your answer. d. To be most effective, the cannonball should hit the galleon right at the waterline (y = 0). At what angle of elevation should the cannonball be fired to accomplish this objective? e. On the Internet or in some other reference source, find out who Sir Francis Drake was, when he lived, and to which country the enemy galleon might have belonged.