Hi guys, I need some help solving the following question using matlab:

My Attempt:

$\displaystyle t_{2}$ is the time at which the object hits the ground (when the height =0, or the root/x-intercept of the graph).

I have to use this Newton Raphson formula:

$\displaystyle

x^k = x^{k-1} - \frac{f(x^{k-1})}{f'(x^{k-1})}

$

so here's my Matlab command:

Code:

theta=pi/4; v=10; g=9.81; a=0.1;
n_itn=3;
y(1)=0;
for k=1:n_itn
y=((1-exp(-a*t))/a)*((g/a)+v*sin(theta))-((g*t)/a)
y'=diff(y)
y(k+1)=y(k)-y(k)/y'(k)
end

But unfortunately I get the following error:

Code:

??? Error: File: Q1.m Line: 6 Column: 3
The expression to the left of the equals sign is not a valid target for an assignment.

I don't understand what's the problem with line 6. Can anyone help?

P.S.

Just to have a confirmation I already tried to estimate the root by ploting y versus t and I think the root is around 1.41, here are my commands:

Code:

theta=pi/4; v=10; g=9.81; a=0.1;
nfinal=2;
t=1:0.01:nfinal;
x=((1-exp(-a*t))/a)*v*cos(theta);
y=((1-exp(-a*t))/a)*((g/a)+v*sin(theta))-((g*t)/a);
plot(t,y,’+')