Missile Defense Project

Calc 3 Scenario

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.

2D Representation of Scenario

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

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.

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

Calculating Initial Velocity

• Using software measured flight path to create known distance

• Started stopwatch on software to measure time

• V=• 38.02 ft/sec

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/

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

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

Rescaled Distance and Time

• vt= 137.48 miles

• vtsinƟ-=0• Rearrange for t• t is 3.101 hours

Initial Velocity

• Calculate Velocity needed to achieve rescaled numbers.

• v = • v = 44.326 mph

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

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>

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)

Time delay

• Operator will not be able to launch the intercepting missile until after 10% of the time has elapsed

• t10% = .3101 hours

Launch Angle

• 3.42= vtsinƟ- solve for v• v = • cosƟ = • Substitute v in cos equation for v equation

Angle and Speed

• Calculated Angle is 36.27 degrees

• Calculate v• v =

• v = 37.55 mph

Mathematica

• Using mathematica and its animation tool show a simulation of missile interception

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