missile defense project.pptx
TRANSCRIPT
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Missile Defense Project
Calc 3 Scenario
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Scenario
• Enemy Site launches a missile in which you must intercept. You know the location of both bases and the target. Calculate an intercept point so the people survive.
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2D Representation of Scenario
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Materials Needed• Materials for pretend scenario:• Tape Measure(100ft)• Video cameras• Water-Bottle Rocket• Water-Bottle Rocket Launcher• Sports Motion Pro-Trainer Program• Mathematica Program• Scientific Calculator• Kinovea Motion Program
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Setup• Simulate an enemy attack by launching water bottles from launcher.• Maintain a centerline and way to calculate angle and initial velocity. Best
way is to record and use motion capture program.• Be sure to measure both distance from launch and off centerline
• Originally recorded for Sports Motion, but used Kinovea due to familiarity with program.
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Reference Measurement
• Ensure an object in full view in recording is measured for calibration while using motion program.
• Measured Case –17.25 inches• Measure angle-angle from vertical axes on
capture. So angle is 90-40=50 degrees
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Calculating Initial Velocity
• Using software measured flight path to create known distance
• Started stopwatch on software to measure time
• V=• 38.02 ft/sec
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Time
• By using the initial velocity and angle from the software, Calculate the time the bottle should have been in flight with only gravity acting on it.
• vtsinƟ-=0• v initial velocity• t is time• Ɵ is angle• g gravity used 32.2 ft/
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Distance
• Calculate distance bottle should have travelled with initial velocity and time calculated.
• D=vtcosƟ• D total distance• V Initial velocity• Ɵ angle
• Calculated at 44.185 ft
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Rescale
• We rescale the scenario to more realistic numbers. Multiple feet by 2 to convert to distance in miles
• Therefore distance is now 88.370 miles
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Rescaled Distance and Time
• vt= 137.48 miles
• vtsinƟ-=0• Rearrange for t• t is 3.101 hours
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Initial Velocity
• Calculate Velocity needed to achieve rescaled numbers.
• v = • v = 44.326 mph
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Total Distance
• Now calculate distance using new velocity and time
• D=vtcosƟ• D = 88.35• The target location is (88.35, 7, 0)• 7 was distance off centerline
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Intercept enemy missile at ¾ travel time
• Must calculate where the enemy missile will be at ¾ travel time
• <¾ vtcosƟ, ¾ d , ¾ vtsinƟ- >
• Intercept point <70.539,5.25,3.42>
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Home Base
• 6 miles away at angle 42 degrees from enemy launch point.
• Calculate coordinates• sinƟ = h = 6 miles• cosƟ = Ɵ = 42 degrees• Home bas location (4.46, 4.01)
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Time delay
• Operator will not be able to launch the intercepting missile until after 10% of the time has elapsed
• t10% = .3101 hours
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Launch Angle
• 3.42= vtsinƟ- solve for v• v = • cosƟ = • Substitute v in cos equation for v equation
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Angle and Speed
• Calculated Angle is 36.27 degrees
• Calculate v• v =
• v = 37.55 mph
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Mathematica
• Using mathematica and its animation tool show a simulation of missile interception
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Saving the World
• Congratulations you have averted a potential disaster
• Pat yourself on the back• Try not to over celebrate
• Thanks goes out to all who helped