Python Programming: An Introduction to Computer Science

10.2. EXAMPLEPROGRAM:CANNONBALL 157

h0 = input("Enterthe initial height (in meters): ")

time = input("Enterthe time interval between position calculations:")

Calculatingtheinitialpositionforthecannonballis alsoeasy. It willstartatdistance0 andheighth0.
We justneeda coupleassignmentstatements.

xpos = 0.0

ypos = h0

Nextweneedtocalculatethexandycomponentsoftheinitialvelocity. We’ll needa littlehigh-school
trigonometry. (See,they toldyouyou’d usethatsomeday.) If weconsidertheinitialvelocityasconsistingof
someamountofchangeinyandandsomeamountofchangeinx, thenthesethreecomponents(velocity, x-
velocityandy-velocity)forma righttriangle.Figure10.1illustratesthesituation.If weknow themagnitude
ofthevelocityandthelaunchangle(labeledtheta, becausetheGreekletterθis oftenusedasthemeasure
ofangles),wecaneasilycalculatethemagnitudeofxvelbytheequationxvel velocitycostheta. A similar
formula(usingsintheta) providesyvel.

velocity yvel = velocity * sin(theta)

theta

xvel = velocity * cos(theta)

Figure10.1:Findingthex andy componentsofvelocity.

Evenif youdon’t completelyunderstandthetrigonometry, theimportantthingis thatwecantranslate
theseformulasintoPythoncode.There’s stillonesubtleissuetoconsider. Ourinputangleis indegrees,and
thePythonmathlibraryusesradianmeasures.We’ll have to convertouranglebeforeapplyingtheformulas.
Thereare 2 πradiansina circle(360degrees);sotheta π

angle
180. Thesethreeformulasgive usthecodefor
computingtheinitialvelocities:

theta = math.pi * angle/ 180.0

xvel = velocity * math.cos(theta)

yvel = velocity * math.sin(theta)

Thatbringsustothemainloopinourprogram.We wanttokeepupdatingthepositionandvelocityof
thecannonballuntilit reachestheground.We candothisbyexaminingthevalueofypos.

while ypos >= 0.0:

I used

astherelationshipsothatwecanstartwiththecannonballontheground(=0)andstillgetthe
loopgoing.Theloopwillquitassoonasthevalueofyposdipsjustbelow 0,indicatingthecannonballhas
embeddeditselfslightlyintheground.
Nowwearrive atthecruxofthesimulation.Eachtimewegothroughtheloop,wewanttoupdatethe
stateofthecannonballtomove ittimesecondsfartherinitsflight.Let’s startbyconsideringmovementin
thehorizontaldirection.Sinceourspecificationsaysthatwecanignorewindresistance,thehorizontalspeed
ofthecannonballwillremainconstantandis givenbythevalueofxvel.
Asa concreteexample,supposetheballis travelingat 30 meterspersecondandis currently 50 meters
fromthefiringpoint.Inanothersecond,it willgo 30 moremetersandbe 80 metersfromthefiringpoint.If
theinterval is only0.1second(ratherthana fullsecond),thenthecannonballwillonlyflyanother 0  1  30  3
metersandbeat a distanceof 53 meters.Youcanseethatthenew distancetraveledis alwaysgivenbytime

• xvel. To updatethehorizontalposition,weneedjustonestatement.

xpos = xpos + time* xvel