The height in meters, y of a projectile, as a function of time is given by y(t) = (mosin() + gr,22)(1-em(t-to))-gm(t-to) +30 where m 10kg is mass of projectile, = 0.1 is the coefficient of friction, to 0 is the initial timing, yo-y(to) 1m is the initial height. g-9.8 is the gravitional constant, vo = 100 is the initial speed, the angle of launch (FYI: The function y(t) is a solution of the differential equation my"(t)t) with constraints y(to)-to and I/(to) = to sin(9).) -mg, 1. (20 points) Write a pseudocode of the bisection algorithm for computing the root of a real valued function. 2. (20 points) Implement your code as a Matlab function using the following input and outputs Input f(z)-The real valued function for which you want to find the root. a, b-An interval for which you think the root lies tol -A tolerance mariter- A maximum number of iterations. Output r- The approximate root of your function (If(r)tol) resarray - An array of the residuals at each step. The first line of your code should therefore read: function Er, resarray] - bisect (f,a,b, tol,maxiter) 3. (20 points) Write a pseudocode of the Newton algorithm for computing the root of a real valued function