MATLAB: Write a script which will calculate the trajectory of a ball thrown at an initial speed vo (ask the user) over a range of angles (θ = 5o − 85o in 5 degree intervals). Make a plot of your trajectories on a single graph.

dynamicsmathsprojectiletrajectory

Not Sure where I'm going wrong here, any advice/solution will be appreciated. I'm quite new to MatLab btw

v0 = input('Enter Initial Velocity of Ball in m/s and Press Return: ');
angle=(5:5:85);
g=9.81;
t=(2*v0.*sin(angle*(pi/180)))/g;
vx = v0.*cos(angle*(pi/180));
vy = v0.*sin(angle*(pi/180));
sx = vx.*t;
sy=vy.*t-0.5*g.*t.^2;
t = 0 : 0.1:100;
plot(sx,sy);

Best Answer

Hi,

to have all the trajectories in one plot you can use:

v0 = input('Enter Initial Velocity of Ball in m/s and Press Return: ');
angle=(5:5:85);
g=9.81;
hold on
for angle = 5:5:85
tges=(2*v0.*sin(angle.*(pi/180)))/g;
t =linspace(0,tges);
vx = v0.*cos(angle.*(pi/180));
vy = v0.*sin(angle.*(pi/180));
sx = vx.*t;
sy=vy.*t-0.5*g.*t.^2;
plot(sx,sy);
end
hold off

result:

as expected the longest distance is given by 45° angle.

Best regards

Stephan

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[k11, k12]=f(x0,y0);     
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MATLAB: How can i solve an equation with an integral when the upper bound is the unknown variable

Hi,

If:

- all variables except t (upper bound) are known,

- assuming that Walter (as usual) is right with his commentary and that arcsine is meant instead of a * sin

- and RO = Ro

you can solve it like this:

syms R2 RO a Ro t vx_t0 vy_t0 t0 vx_t1 vy_t1 t1
f = asin((R2+RO)*sin(a)/(2*RO))*RO == int(t1*sqrt(vx_t1^2+vy_t1^2)) - int(t0*sqrt(vx_t0^2+vy_t0^2))

divides the integral into the upper - lower bound with the corresponding variables. When solving for t1 and simplifying the result you get:

sol_t1 = t1 == simplify(solve(f,t1))

or as a function handle:

t1_fun = @(R2,RO,a,t0,vx_t0,vx_t1,vy_t0,vy_t1)(RO.*asin((sin(a).*(R2+RO).*(1.0./2.0))./RO).*2.0+t0.*vy_t0.^2.*log(vx_t0+sqrt(vx_t0.^2+vy_t0.^2))+t0.*vx_t0.*sqrt(vx_t0.^2+vy_t0.^2))./(vx_t1.*sqrt(vx_t1.^2+vy_t1.^2)+vy_t1.^2.*log(vx_t1+sqrt(vx_t1.^2+vy_t1.^2)))

Of course, this only works if the above conditions are met. Then you can calculate your upper limit (here: t1) in this way.