AA Simulation: Firing Range
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1 America's Army walkthrough AA Simulation: Firing Range Firing Range This simulation serves as an introduction to uniform motion and the relationship between distance, rate, and time. Gravity is removed for this simulation to help focus the learning on motion in one direction. Concept 1: Uniform motion can be modeled by the formula Distance = Rate * Time (D=Rt) The Firing Range simulation does not focus on the difference between displacement and distance or velocity and speed. Concept 2: The rate of horizontal motion is constant. The rate at which the fired round is traveling just after launch will remain the same until impact. The only way for the round to slow down is if another force acts upon it. Something would have to hit the round, or wind resistance would need slow it down. In this exercise there is no wind resistance, so the fired round will not slow down until impact. Simulation Tips and Example Problems Find time given distance and rate. Distance Formula Rearrange the formula to solve for time by dividing both sides of the equation by R AA Simulation: Firing Range Page 1
2 ()(yy221the simulation runs in real time. For example, if the formula calls for a time of 5.32s, the simulation will take 5.32s from firing to impact. If the target falls over, then your answer is too high and the round collided with the target before detonating. If your answer is too low, the round will detonate before hitting the target. There is a +/-.02 tolerance for correct answers AA Simulation: Mountain Pass Mountain Pass Students are introduced to the formulas for motion in two directions. The purpose of the simulation is to serve as an introduction to the concept of projectile motion and to provide practice using the formulas. All projectiles follow the path of a parabola assuming that no other forces are acting on the projectile. In this simulation students will calculate the horizontal displacement (also called range). If the firing angle is given, then calculate the initial velocity. If the initial velocity is given, then calculate the firing angle. Concept 1: Horizontal displacement (d) is also known as range (x). 2Range x = xxx21 + V2sinθxi-g2= )= Concept 2: If the firing angle and range are known, then the initial velocity may be predicted. -xginitial velocity isin2= Vθ Concept 3: If the range and initial velocity are known, then the firing angle may be predicted. -xgfiring angle sin1 θ= V2 i 2Simulation Tips and Example Problems AA Simulation: Firing Range Page 2
3 It is assumed that the tank and the target are on the same horizontal plane. If you enter incorrect answers, the simulation will behave accordingly. For example, if you enter a 90 degree firing angle, the round will fire mstraight up. Acceleration due to gravity g9.81 s= 2Find range using the displacement formula. Range formula Substitute Note: x-y axis is on a horizontal plane from tank to target Solve. The final answer is the range or displacement from tank to target.. Enter the range the answer blank. Find the initial velocity (V i ) given the firing angle after solving for range. Range (x) = m Initial velocity formula Substitute Solve AA Simulation: Firing Range Page 3
4 Find the firing angle ( θ ) given the initial velocity after solving for range. Range (x) = m -xgsin1 Firing angle formula θ= V2 i 2Substitute Solve.. xg Note: V2must equal a value between 0 iand 1. If the calculator gives an error, this is likely the cause. Answers are rounded to the nearest with a +/-.02 tolerance AA Simulation: Firing Range Page 4
5 Vin(((θ())iOptional: The following process outlines the steps for rearranging the initial velocity equations to solve for the firing angle. -xginitial velocity formula 2θV-xgSquare both sides of the equation 2sin)= 2isin= sin2θv-xg= Multiply both sides of the equation by -xgsin(2θ) i2v2iθsv2divide both sides of the equation by i-g1s1inverse sine both sides of the equation ( ) ixsinn2 θ = V2 i s-xgsin1firing angle formula θ = V2 i 22i)= naa Simulation: Parachute Drop Parachute Drop The purpose of the Parachute Drop simulation is to introduce students to acceleration due to gravity and to further develop their understanding of velocity. Concept: An object in freefall experiences acceleration due to gravity. Acceleration is the rate at which an object changes velocity. Simulation Tips and Example Problems: Terminology: Height Deployment height Freefall distance Freefall time The height of the helicopter. The height at which the parachute deploys. The distance between the helicopter and the point where the parachute deploys. The amount of time that the package is in freefall. AA Simulation: Firing Range Page 5
6 8mDeployment time Total Time Deployment velocity Acceleration due to gravity The amount of time between deployment and when the package hits the ground. The sum of freefall and deployment time. The rate at which the package falls with the parachute deployed. Rate of acceleration of an object in freefall. mg9.81 s= 2Formulas 1used: tg2 D2= Distance when package is in freefall Deployment Height = Deployment velocity * Deployment time (D=V * t) Freefall Height = Freefall velocity * Freefall time (D=V * t) Total time = Freefall time + Deployment time Height = Freefall distance + Deployment height Displacement during deployment Displacement during freefall Total time The height of the helicopter Example Problem 1: Find freefall time Total time = Freefall time + Deployment time Freefall time = Total time Depl- oydeployment mentheighttime eploymentimedeploymentvelocity=dtotal time formula Rearrange to solve for freefall time Deployment time formula 94.4Frefaltime24.90 s= m5.0 Freefall time = 6.00s s Note: answers are rounded to the AA Simulation: Firing Range Page 6
7 nearest Find freefall distance 1tg2 D2= 1m9.6.0s( ) 22s 2 = 81Freefall distance formulas D = m Find the height of the helicopter Height = Freefall distance + Deployment distance H = m m H = m Helicopter height formula Note: The total time is 24.90s. It will take this long for the box to hit the ground, so be patient. You won t know if your answer is correct until the box hits the ground. If the box smashes, then your answer was wrong. Example Problem 2: Find freefall distance 1tg2 D2= Freefall distance formula 1D9.= 2 D = 78.48m 81m4s.02( ) 20s AA Simulation: Firing Range Page 7
8 Find deployment distance Height = Freefall distance + Deployment distance Helicopter height formula Deployment distance = Height - Freefall distance Rearrange to solve for deployment distance Deployment distance = m m Deployment distance = 41.82m Find deployment velocity AA Simulation: Firing Range Page 8 Deployment Height = Deployment velocity * Helicopter height formula Deployment time (D=V * t) Rearrange to solve for deployment DeploymentheightDeploymentvelocityDeploymenttime= velocity Subtract total time from freefall time to solve for deployment time DeploymentheightDeploymentvelocityTotaltimeFreefaltime(= )41.82meploymentvelocityD17.94s4.00s(= ) meploymentvelocity3.00s=dnote: answers are rounded to the nearest
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