How do I create a projectile motion function with the input of angle which is scalar, and time which is a vector.

function [x,y]=trajectory(a,time)
x0=0
y0=0
k=0
angle=a*(pi./180)
v=70
g=9.81
t=0:0.1:time
x=x0+v*cos(angle)*t;
y=y0+v*sin(angle)*t-(g*t.^2)/2
figure
plot(x,y)
end

So far I have this code, which succesfully plots the graph of a projectile at the given velocity (v) and constant (g) The input is (a) which is angle and (time) which is the amount of seconds after launch. I got stuck here because in the input (a) has to stay a scalar but (time) has to be a vector, so I can input more values for time, and the output would be more graphs with the same (a) angle, but in different times since the launch.

How can I make (time) a vector and have more plotted graphs as the output?

[Jan]

The question is not clear. The trajectory is evaluated for a time vector already: t = 0:0.1:time . Definint time as a vector is not meaningful in consequence, while a variatin of the angle would be interesting.

[Image Analyst]

time is the name of a built-in function so you should not use it as the name of your variable. Call it totalTime or elapsedTime or timeOfFlight instead.

Answer 1

[Jan]

You can move the commands for creating the diagram from the function to the caller:

function main

figure;
AxesH = axes('NextPlot', 'add');
time  = 20;
[x,y] = trajectory(10, time)
plot(x, y, 'r', 'Parent', AxesH)
[x,y] = trajectory(20, time)
plot(x, y, 'b', 'Parent', AxesH)
end

function [x,y]=trajectory(a,time)
x0=0;
y0=0;
% k=0 ???
angle=a*(pi./180)
v=70;
g=9.81;
t=0:0.1:time
x=x0+v*cos(angle)*t;
y=y0+v*sin(angle)*t-(g*t.^2)/2;
end

You can vary the angle in a loop also. And if you really want to vary the time, this can be done equivalently.

[Surik Ahmed]

can you help me please. I have an equation by Mathieu & analytic solutions

Answer 2

[Image Analyst]

OK, now that your homework problem is well over, here is my solution. Granted, it's a bit fancier than a typical beginner would do, but I'm an overachiever.

It computes just about everything that you could possibly want to know about the trajectory for a single angle. Then it computes and plots trajectories for several angles. You can delete anything that you don't need to know to make it simpler. The code is extremely well commented so you should have no trouble following it.

The projectile.m file is attached below these two images that it creates. If you like it, please "Vote" for my answer.

[Jean Ramirez]

Awesome code. Thanks!

[Finn Johnston]

I am assuming that velocity is in metres per second?

[Image Analyst]

Yes, since acceleration is 9.8 m/sec^2, everything else is in meters and seconds. It also says that when you enter the velocity - it tells you the units to use.

I've made a few slight improvements like adding the units to the axes labels. The latest one is attached.

[Xinran Deng]

Really awesome work!!! But could you please help me modify it to take air resistance into account?

I aim to compare the two formulae: f=kv and f=kv^2

Could you give me advice that how can I modify your version to draw the trajectory considering air resistance?

I love your presentation of nice graphs sooooo much!!!

[Mena Nabil]

i made an account to upvote your answer thanks sir.

[Anon]

you have absolutely saved me! thank you so much !!

[Ali Madkhali]

how i can make the same but with an obstacles like wall in the way?

[Image Analyst]

@Ali Madkhali you just have to define some x and y region for the obstacle, then see if the trajectory enters that region.

if x > xObstacle & y < yObstacle
    % It would be inside the obstacle, so do something...
end

If it does, bounce it off or just truncate the trajectory at that point. Sorry but I don't have a demo for that.