Launch a particle from ground level with some speed and some angle and compute the trajectory using numerical integration. This is a very simple example for those learning to program.

importmath# Constantsg=10.0# gravityv0=20.0# initial speedtheta0=math.pi/4.0# initial angledt=10.0**(-5.0)# time step######################################## Initialize simulationt=0.0# timecount=0# count for printingx=0.0# initial positiony=0.0xd=v0*math.cos(theta0)# initial velocityyd=v0*math.sin(theta0)xdd=0.0# initial accelerationydd=-g######################################## Run simulationwhiley>=0.0:# run while object in flight# numerical integration# explicit Eulerx=x+xd*dt# update position based on velocityy=y+yd*dtxd=xd+xdd*dt# update velocity based on accelerationyd=yd+ydd*dtxdd=0.0# constant acclerationydd=-gt=t+dt# advance time and countcount=count+1ifcount%1000==0:# print once every thousand simulation intervalsprintt,x,y

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print"import math#constantg=10.0#gravityv0=20.0#initial speedtheta0=math.pi/4.0#initial speeddt=10.0**(-5.0)#time step###########################################Initial simulationt=0.0#timecount=0#count for printingx=0.0#initial positiony=0.0xd=v0*math.cos(theta0)#initial velocityyd=v0*math.sin(theta0)xdd=0.0#initial accelerationydd=-g###############################################Run simulationwhiley>=0.0:#run while object in flight#numerical integration#elpicit eulerx=x+xd*dt#update position based on velocityy=y+yd*dtxd=xd+xdd*dt#update velocity based on accelerationyd=yd+ydd*dtxdd=0.0#constanrt accelerationt=t+dt#advance time and countcount=count+1ifcount%1000==0:#print once every thousand simulation intervalsprint(t,x,y)"

@A Former Brilliant Member
–
You're welcome. And the cool part is that nowhere in the code is any parabola explicitly specified or coded. It just comes out of the numerical integration

@Steven Chase okay! thanks , can you please give me some questions or post for practicing numerical integration .
if you post it should be of E and M.
THANKS IN ADVANCE

Easy Math Editor

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## Comments

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TopNewest@Steven Chase thanks sir

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@Steven Chase sir i have also typed the the whole code ,but my code is not expressed as your code is expressed in brilliant ??

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You need three ticks and then "Python", and then code, followed by three more ticks

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@Steven Chase sir can you please show a photo of your excel ,i am facing a bit of difficulty while plotting it in excel.

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You have to import the data from a text file and choose space-delimited format

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@Steven Chase i stucked here

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Insert - Scatter - Scatter with smooth lines

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@Steven Chase which option should I choose here

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@Steven Chase which option

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@Steven Chase now where I have to go?

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Insert - scatter chart - scatter with smooth lines

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I was going to that scatter only by mistake my arrow is at (other charts)

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@Steven Chase

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There it is

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@Steven Chase yes, Thank you sir

I don't think that anyone in the universe will help me like this you have helped me.

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@Steven Chase yeah it is interesting

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@Steven Chase sir in the last 2nd step what is the meaning of that double equal to = = ??

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I single equals sign is used to declare the value of a quantity. A double equals sign is used to compare two quantities to see if they are equal

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@Steven Chase okay! thanks , can you please give me some questions or post for practicing numerical integration .

if you post it should be of E and M.

THANKS IN ADVANCE

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Wow you're such a dedicated student. Really awesome to see passion and dedication :)

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@Steven Chase I want to learn monte Carlo, how can I learn??

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Hey! You can check out this book.

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@Aaghaz Mahajan Thanks bro for this book

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