FlyBy Math Simulator Worksheet E - Page 1 of 6 EG-2004-11-111-ARC

Student Worksheet E

Analyzing a Distance vs. Time Graph for Two Planes

In this worksheet, you will work with 2 planes. Sometimes you will work with

1 jet route; other times you will work with 2 jet routes.

Each jet route is 20 feet long.•The jet routes meet at the 20-foot mark.•Theplanesareflyingatthesamealtitude.•Theplanesareflyingatdifferentspeeds.•Theplaneshavedifferentstartingpositions.•

You will use the simulator to learn:

What happens in the • Jet Route Panel when two lines cross in the Graph Panel. (Dothetwoplanescollideornot?)

Name _________________________ Answers

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Exploring the Simulator

In the Graph Panel,dragthetimeslider( )untiltheNAL63dotisontopoftheWAL27dotwhere the lines cross. Then answer these questions.

(a) In the Jet Route Panel,dotheplanescollide? Yes No

(b)DONOTRESETtheproblem.IntheJet Route Panel,chooseTWO(2)jetroutes.

In the Jet Route Panel,dotheplanescollide? Yes No

(c) Fillintheblanktocompleteeachsentence.

With onejetroute,thelinescrossedonthegraphandtheplanes collide. (did/didnot)

With twojetroutes,thelinescrossedonthegraphandtheplanes collide. (did/didnot)

Problem 1: Set up the simulator

Timeslider: 0seconds•

2 planes, • 1 route

WAL27startingposition: 1ft•

NAL63startingposition: 7ft•

MakesuretheNAL63linecrossestheWAL27linesomewherenearthecenterof•the Graph Panel. (You may need to grab and rotate one or both lines.)

did

did not

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Analyzing What Happens on the Jet Route(s) When Two Lines Cross on the Graph

In the Graph Panel,dragthetimesliderto20secondssotheWAL27dotandtheNAL63dotare at the point where the lines cross. Then answer these questions.

(a) IntheGraph Panel,thelinescrosswhentimex=20seconds.

In the Jet Route Panel:

Dotheplanescollide? Yes No

HowfarisWAL27fromthestartofthejetroute? ft

HowfarisNAL63fromthestartofthejetroute? ft

Arethesedistancesthesame? Yes No

(b) IntheGraph Panel, at the point where the lines cross, what is the y-coordinate foreachplane?

WAL27: (x,y)=(20seconds,_________ft)

NAL63: (x,y)=(20seconds,_________ft)

(c) DONOTRESETtheproblem.IntheJet Route Panel,chooseTWO(2)jetroutes. In the Graph Panel,thelinescrosswhentimex=20seconds.

In the Jet Route Panel:

Dotheplanescollide? Yes No

HowfarisWAL27fromthestartofitsjetroute? ft

HowfarisNAL63fromthestartofitsjetroute? ft

Arethedistancesthesame? Yes No

Problem 2: Set up the simulator

Timeslider: 0seconds•

2 planes, • 1 route

WAL27start: 0ft,• 1/2ft/sec

NAL63start: 5ft,• 1/4ft/sec

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Problem 3:

Two Jet Route Panels are shown.

(a)Checkalltheplaceswheretwoplanescouldcollideonone jet route.

qAt 0 feet, where the route begins.

q At20feet,wheretherouteends.

q Anywhere else along the route.

(b)Checkalltheplaceswheretwoplanescouldcollideonthesetwo jet routes.

qAt 0 feet, where each route begins.

q At 20 feet, where the routes meet.

q Anywhere else along the routes.

Summarizing What Happens on the Jet Route(s) When Two Lines Cross on the Graph

Problem 4:

A graph for two planes is shown.

(a)WAL27andNAL63areflyingonthesame 20-foot jet route.

Thelinescrossonthegraphaty=15feet.

Dotheplanescollideonthejetroute?

Yes No

(b)WAL27andNAL63areflyingondifferent jet routes that meet at 20 feet.

Thelinescrossonthegraphaty=15feet.

Dotheplanescollideonthejetroutes?

Yes No

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Problem 5:

A graph for two planes is shown.

(a)WAL27 andNAL63 are flying ondifferent jet routes that meet at 20 feet.

The lines meet on the graph at y = 20 feet.

Dotheplanescollideonthejetroutes?

Yes No

Howdoyouknow?

Problem 6: SUMMARIZE

(a)Checkthesentencesforwhichyouaresure that two planes do collide.

qIn the Graph Panel, the two lines cross or meet.

q IntheGraphPanel,thetwolinesareparallel.(Thelineshavethesameslope.)

q In the Graph Panel, the two lines cross or meet; in the Jet Route Panel, the planes are on the same route.

q In the Graph Panel, the two lines cross or meet; in the Jet Route Panel, the planes are on different routes that meet at an intersection.

(b)Checkthesentencesforwhichyouaresure that two planes do NOT collide.

qIn the Graph Panel, the two lines cross or meet.

q IntheGraphPanel,thetwolinesareparallel.(Thelineshavethesameslope.)

q In the Graph Panel, the two lines cross or meet; in the Jet Route Panel, the planes are on the same route.

q In the Graph Panel, the two lines cross or meet; in the Jet Route Panel, the planes are on different routes that meet at an intersection.

The lines meet at a point where y = 20, so each plane is at the 20-foot mark on its

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jet route at the same time. Since the two routes meet at that 20-foot mark, the planes collide.

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Problem 7:

GOBEYOND: Checkallthedifferentsituationsthatcouldberepresentedbythisgraph.

qTwoplanesflyingonthesamejetroute.

q Twoplanesflyingondifferentjetroutesthatmeet.

q Twoplanesflyingondifferentjetroutesthatdonotmeet.

q Twocarsdrivingondifferentroads.

q Twotrainsonthesametracktravelingtowardeachother.

q Twotrainsondifferenttrackstravelingawayfromeachother.

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