Write a MATLAB script that plots the function f(m) versus m. Assume a drag coefficient of 0.35 kg/m and for the bungee jumper to have a velocity of 40 m/s after 5s of free fall.
1. In the absence of air resistance the Cartesian coordinates of a projectile launched Show more PLAESE HELP 1. In the absence of air resistance the Cartesian coordinates of a projectile launched with an initial velocity v0 (m/s) and angle 0 (degrees) can be computed with x = v0 cos(0)t y = v0 sin(0)t 0.5gt2 where g is the gravitational acceleration (= 9.81 m/s 2 ) and t is the time (s). Assume that v0 = 8 m/s and write a well commented MATLAB script to generate a plot of the projectiles trajectory for various initial angles ranging from 60 to 75 in increments of 5 . Note that 0 is in degrees and so use the appropriate MATLAB functions sind and cosd to obtain the corresponding trigonometric values. Generate a vector for t from 0s to 8s in increments of 1/128s. Generate a single plot of the height achieved (y) versus horizontal distance (x) for each of the initial angles. Label the axes appropriately and use a legend to distinguish among the different cases. Scale the plot such that the minimum height is zero using the axis command. The following plot shows two such trajectories corresponding to launch angles of 60 and 75 respectively 2. Medical studies have established that a bungee jumpers chances of sustaining a significant vertebrae injury increase significantly if the free-fall velocity exceeds 40 m/s after 5s of free fall. Your boss at the company wants you to determine the mass at which this criterion is exceeded given a drag coefficient of 0.35 kg/m. The following analytical equation can be used to predict fall velocity as a function of time: v(t) = r g m Cd tanh t r g Cd m ! Here v is the downward vertical velocity (m/s) t is the time (s) g is the acceleration due to gravity (= 9.81 m/s2 ) Cd is the drag coefficient (kg/m) and m is the jumpers mass (kg). Try as you might you cannot manipulate this equation to explicitly solve for mthat is you cannot isolate the mass on the left side of the equation. So an alternative way of looking at the problem involves subtracting v(t) from both sides to give a new function: f(m) = r g m Cd tanh t r g Cd m ! v(t) We can now see that the answer to the problem posed by your boss is the value of m that makes the above function equal to zero. A simple and graphical approach for obtaining an estimate of the root of the equation f(m) = 0 is to make a plot of the function and observe where it crosses the x axis. This point which represents the mass value for which f(m) = 0 provides a rough approximation of the root. Answer the following questions. Write a MATLAB script that plots the function f(m) versus m. Assume a drag coefficient of 0.35 kg/m and for the bungee jumper to have a velocity of 40 m/s after 5s of free fall. Your output should look similar to the plot shown below when the mass is varied from 50 to 200 kg. Use an algorithmic method to obtain the root automatically within your MATLAB code that is you must not attempt to obtain the root via visual observation. Your code should achieve this by examining the vector containing the output values f(m) and by pinpointing the value of m for which f(m) is closest to zero. Use a fprintf statement to print this value. Your answer should be accurate to three decimal places. Prepare a well-commented MATLAB script for each problem Show less
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