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Problem 3: Applied Problem: Rocket and Air Resistance The purpose of this problem is to apply Newton's method to find characteristic times of an application. The equation models the height of a rocket from the ground at time t, if it is ejected at timet 0 with some initial speed h(t) =-331+ 784( 1-e-0.3t) and is subject to air resistance. See Figure 2 for a plot of h(t) as a function of time. In your prob30, do the following (a) Using RevtonMethod1D, approximate the time at which the rockst hits the cround. Report your resmults using fprintf, and descriptive text. (b) Using NewtonMethod1D, approximate the time at which the rocket hits its maximum height and compute the maximum height. Report your results using fprintf, and descriptive text. c)Produce a plot like the one in Figure 2, with the maximum height and the time the rocket hits the ground (as approximated by Newton's method) clearly marked. For this problem, you may make your own choices for tol and maxIter, as long as they give reasonable answers. Problem 3: Applied Problem: Rocket and Air Resistance The purpose of this problem is to apply Newton's method to find characteristic times of an application. The equation models the height of a rocket from the ground at time t, if it is ejected at timet 0 with some initial speed h(t) =-331+ 784( 1-e-0.3t) and is subject to air resistance. See Figure 2 for a plot of h(t) as a function of time. In your prob30, do the following (a) Using RevtonMethod1D, approximate the time at which the rockst hits the cround. Report your resmults using fprintf, and descriptive text. (b) Using NewtonMethod1D, approximate the time at which the rocket hits its maximum height and compute the maximum height. Report your results using fprintf, and descriptive text. c)Produce a plot like the one in Figure 2, with the maximum height and the time the rocket hits the ground (as approximated by Newton's method) clearly marked. For this problem, you may make your own choices for tol and maxIter, as long as they give reasonable answers