The problem:

A projectile is fired from the origin with a speed of $15\frac{m}{s}$ at hits a target located at $(x,y)=(30,5)m.$ The equations that communicate this are

$30=15cos()t$

$5=15sin()t-\frac{1}{2}(9\mathrm{.}81)t^2$

This is non$-$linear system of $2$ equations, $2$ unknowns for $$ and $t.$ I$\text{'}$d like you to solve this two ways:

a$)$ Solve the above using fixed point iteration. Use an initial guess of $=30,$ solving for $t$ in the first equation, and then substituting that $t$ value in the second equation to solve for a new $$ guess. Repeat this process ten times and store the solutions $$ on HW$\{1\}$ and $t$ on $HW\{2\}.$

b$)$ Solve the above using secant method. Solve the first equation for $t,$ substituting algebraically into the second equation, generating a $1$ equation $1$ unknown situation. Use an initial guess of $=30,$ and iterate until Save your $$ on $HW\{3\}$ and your $t$ on $HW\{4\}$

In the above, all algebraic work must be done by you. Matlab won't do your algebra!