Lab 5: Computer Simulation of Projectile Motion: Integrating at the ArcadeJeremy JohnsonDue Wed. Mar. 15 by 11:55 pm (you have two weeks to complete this lab)In this lab you will write Maple procedures that simulate the firing of a human cannonball being shot at a target. The motion of the cannonball is determined by equations of motion that can be solved using integration (see section 6.7 of the Anton text). Maple's animate command can be used to easily produce a simulation which shows the cannonball flying towards the target. Whether the cannonball hits the target or not depends on the initial velocity of the cannonball and the angle of elevation of the cannon, and the simulation takes these two parameters and shows the outcome. The introduction to this lab reviews the equations of motion and shows how to use animate for a similar problem. In this problem, a ball is shot straight up in the air towards a target and depending on the target height and the initial velocity the ball will hit or miss the target. This game is similar to the arcade game where the contestant uses a hammer to launch a disk towards a bell, thus measuring the "strength" of the contestant. If you understand the example in the introduction, both the mathematics and maple coding, you should be able to do the cannon simulation. After going through the introduction, you and your partner should first plan out how you will solve the cannon ball problem and review the mathematics behind it, prior to working on the Maple code.
<Text-field style="Heading 1" layout="Heading 1">Introduction: Test your Strength and Knowledge</Text-field>In this section, we derive the equations of motion for the arcade game where the contestant uses a hammer to launch a disk straight up towards a bell which is a certain distance from the ground. If the contestant hits the launch pad hard enough, the disk will reach the bell and he or she wins. In our simulation of this game, we will assume that after hitting the launch pad the disk will head towards the bell with an initial velocity, which will be specified rather than simulating the hammer, and the only force bringing it back down is gravity. We need to find equations that model the position of the disk and will use these equations to 1) determine if the disk reaches the bell, 2) plot the trajectory of the disk as a function of time, and 3) animate the motion of the disk so that we can simulate the behavior of the game.An object under the force of gravity accelerates towards the Earth at a rate of 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Acceleration is the rate of change in the velocity, and the velocity, 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the object as a function of time can be determined from the following equation: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which can be solved by integrating each sideLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYvLUkjbWlHRiQ2OVEhRicvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lJXNpemVHUSMxMkYnLyUlYm9sZEdRJmZhbHNlRicvJSdpdGFsaWNHUSV0cnVlRicvJSp1bmRlcmxpbmVHRjcvJSpzdWJzY3JpcHRHRjcvJSxzdXBlcnNjcmlwdEdGNy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnLyUnb3BhcXVlR0Y3LyUrZXhlY3V0YWJsZUdGNy8lKXJlYWRvbmx5R0Y3LyUpY29tcG9zZWRHRjcvJSpjb252ZXJ0ZWRHRjcvJStpbXNlbGVjdGVkR0Y3LyUscGxhY2Vob2xkZXJHRjcvJTBmb250X3N0eWxlX25hbWVHUSgyRH5NYXRoRicvJSptYXRoY29sb3JHRkMvJS9tYXRoYmFja2dyb3VuZEdGRi8lK2ZvbnRmYW1pbHlHRjEvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUpbWF0aHNpemVHRjQtRiM2JS1GLDY5USJ2RidGL0YyRjVGOEY7Rj1GP0ZBRkRGR0ZJRktGTUZPRlFGU0ZVRlhGWkZmbkZobkZbby1JI21vR0YkNjNRMCZBcHBseUZ1bmN0aW9uO0YnLyUlZm9ybUdRJmluZml4RicvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lJ2xzcGFjZUdRJDBlbUYnLyUncnNwYWNlR0ZfcC8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobWF4c2l6ZUdRKWluZmluaXR5RicvJShtaW5zaXplR1EiMUYnLyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJTBmb250X3N0eWxlX25hbWVHRlcvJSVzaXplR0Y0LyUrZm9yZWdyb3VuZEdGQy8lK2JhY2tncm91bmRHRkYtSShtZmVuY2VkR0YkNiMtRiM2Iy1GLDY5USJ0RidGL0YyRjVGOEY7Rj1GP0ZBRkRGR0ZJRktGTUZPRlFGU0ZVRlhGWkZmbkZobkZbby1GY282M1ExJkludmlzaWJsZVRpbWVzO0YnRmZvRmlvRltwL0ZecFEvdGhpY2ttYXRoc3BhY2VGJy9GYXBGZnJGYnBGZHBGZnBGaXBGXHFGXnFGYHFGYnFGZHFGZnFGaHEtRmNvNjNRIj1GJ0Zmb0Zpb0ZbcEZlckZnckZicEZkcEZmcEZpcEZccUZecUZgcUZicUZkcUZmcUZocS1GY282M0ZkckZmb0Zpb0ZbcC9GXnBRMG1lZGl1bW1hdGhzcGFjZUYnL0ZhcEZec0ZicEZkcEZmcEZpcEZccUZecUZgcUZicUZkcUZmcUZocS1GIzYpLUZjbzYzUSsmSW50ZWdyYWw7RicvRmdvUSdwcmVmaXhGJ0Zpb0ZbcEZdcEZgcC9GY3BGOkZkcEZmcEZpcC9GXXFGOkZecUZgcUZicUZkcUZmcUZocS1GLDY5USsmdW1pbnVzMDtnRidGL0YyRjVGOEY7Rj1GP0ZBRkRGR0ZJRktGTUZPRlFGU0ZVRlhGWkZmbkZobkZbby1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EnMC4wfmV4RicvJSZ3aWR0aEdRJzAuNX5lbUYnLyUmZGVwdGhHRmF0LyUqbGluZWJyZWFrR1ElYXV0b0YnLUZjbzYzUTAmRGlmZmVyZW50aWFsRDtGJ0Zlc0Zpb0ZbcEZdcEZgcEZicEZkcEZmcEZpcEZccUZecUZgcUZicUZkcUZmcUZocUZfckZici9JK21zZW1hbnRpY3NHRiRRJGludEYnRmhyLUYsNjlRLCZ1bWludXMwO2d0RidGL0YyRjVGOEY7Rj1GP0ZBRkRGR0ZJRktGTUZPRlFGU0ZVRlhGWkZmbkZobkZbb0Zbcy1GY282M1EnJnBsdXM7RidGZm9GaW9GW3BGXXNGX3NGYnBGZHBGZnBGaXBGXHFGXnFGYHFGYnFGZHFGZnFGaHEtRmNvNjNGZHJGZm9GaW8vRlxwRjpGXXAvRmFwUTN2ZXJ5dGhpY2ttYXRoc3BhY2VGJ0ZicEZkcEZmcEZpcEZccUZecUZgcUZicUZkcUZmcUZocS1GLDY5USJDRidGL0YyRjVGOEY7Rj1GP0ZBRkRGR0ZJRktGTUZPRlFGU0ZVRlhGWkZmbkZobkZbby1GY282M1EiLEYnRmZvRmlvRmh1Rl1wRml1RmJwRmRwRmZwRmlwRlxxRl5xRmBxRmJxRmRxRmZxRmhxwhere 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is the constant of integration. We can solve for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2OVEiQ0YnLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRicvJSVzaXplR1EjMTJGJy8lJWJvbGRHUSZmYWxzZUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUqdW5kZXJsaW5lR0Y3LyUqc3Vic2NyaXB0R0Y3LyUsc3VwZXJzY3JpcHRHRjcvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GJy8lJ29wYXF1ZUdGNy8lK2V4ZWN1dGFibGVHRjcvJSlyZWFkb25seUdGNy8lKWNvbXBvc2VkR0Y3LyUqY29udmVydGVkR0Y3LyUraW1zZWxlY3RlZEdGNy8lLHBsYWNlaG9sZGVyR0Y3LyUwZm9udF9zdHlsZV9uYW1lR1EoMkR+TWF0aEYnLyUqbWF0aGNvbG9yR0ZDLyUvbWF0aGJhY2tncm91bmRHRkYvJStmb250ZmFtaWx5R0YxLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lKW1hdGhzaXplR0Y0LUkjbW9HRiQ2M1ExJkludmlzaWJsZVRpbWVzO0YnLyUlZm9ybUdRJmluZml4RicvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lJ2xzcGFjZUdRL3RoaWNrbWF0aHNwYWNlRicvJSdyc3BhY2VHRmpvLyUpc3RyZXRjaHlHRjcvJSpzeW1tZXRyaWNHRjcvJShtYXhzaXplR1EpaW5maW5pdHlGJy8lKG1pbnNpemVHUSIxRicvJShsYXJnZW9wR0Y3LyUubW92YWJsZWxpbWl0c0dGNy8lJ2FjY2VudEdGNy8lMGZvbnRfc3R5bGVfbmFtZUdGVy8lJXNpemVHRjQvJStmb3JlZ3JvdW5kR0ZDLyUrYmFja2dyb3VuZEdGRg==using the initial 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 implies that 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In our situation, the initial velocity is determined from how hard the launch pad is hit, and will be specified as an input to our simulation. Since velocity is the rate of change of position, 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 with respect to time, the position of the ball can be determined from the 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, again, can be solved by integrating each 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where 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which in our case is equal to 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since the ball starts on the ground.The time when the maximum height of the disk is reached can be determined by solving the equation 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and the time when the disk returns to the ground is obtained from the equation 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Note that there are two times when the disk is on the ground: at time equal to zero and at a later time when the disk returns to the ground. It is easy to show that the time when the disk returns to the ground is twice the time when the disk reaches the maximum height [why?].The following Maple computations use these equations to determine the trajectory of the disk for different initial velocities. Once the equation, 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for the position is obtained, we can plot the trajectory. We can also visualize the simulation of the disk using Maple's animate command. with(plots);g := 32; a := -g;s0 := 0; v0 := 'v0';v := int(a,t) + v0;s := int(v,t)+s0;tmax := solve(v=0,t);smax := subs(t=tmax,s);