Have to find the answers by coding in Matlab
In this problem, there are three raptors, denoted by r0, r1 and r2, at the corner of an equilateral triangle and you are standing in the middle. Specifically, we assume the coordinates of r0, r1 and r2 are (d, 0), (-d/2, d squareroot 3/2) and (-d/2,-d squareroot 3/2), respectively. Your coordinate is (0, 0). That is, the distance between you and any of the raptors is d meters. The raptors all run towards you at different speeds with r0, r1 and r2 being 12 m/s, 10 m/s and 15 m/s, respectively Your speed is 8 m/s. Assume that you only pick your direction in the beginning (it cannot be changed after the initial selection). Find the direction that maximizes your survival time (you can use the code given to you as the starting point). What is the optimal direction (to within a degree) and how long before you get eaten by one of the raptors. For this case, also show the plot of all entities and their movement. Show the plot for d = 30 for the best angle, and print the time. Also, write the equations governing the movement of raptors. Changing the scenario in Problem 1, we now assume that you can change your direction as well. Your run for a fixed period of time (say, dt). After this, you re-evaluate your direction to pick the best direction from that instant. You keep running in this manner. How long before you get caught? Plot the trajectories for this case for dt = 0.01s. All other parameters stay the same. Highlight changes in equations from solution to problem 1. In this problem, there is only one raptor, which is on the same line as you (say, x-axis). The raptor spots you 50 meters away and runs towards you, accelerating at 4 m/s^2 up to its maximum speed of 25 m/s. You run with an acceleration of 2 m/s^2 and your maximum speed is 8 m/s. How long before you get caught? Write a Matlab program to simulate this process. Furthermore, if the distance between you and the raptor is d meters and it takes time of t seconds before you get caught, write a mathematical expression of t in terms of the distance d. In this problem, there are three raptors, denoted by r0, r1 and r2, at the corner of an equilateral triangle and you are standing in the middle. Specifically, we assume the coordinates of r0, r1 and r2 are (d, 0), (-d/2, d squareroot 3/2) and (-d/2,-d squareroot 3/2), respectively. Your coordinate is (0, 0). That is, the distance between you and any of the raptors is d meters. The raptors all run towards you at different speeds with r0, r1 and r2 being 12 m/s, 10 m/s and 15 m/s, respectively Your speed is 8 m/s. Assume that you only pick your direction in the beginning (it cannot be changed after the initial selection). Find the direction that maximizes your survival time (you can use the code given to you as the starting point). What is the optimal direction (to within a degree) and how long before you get eaten by one of the raptors. For this case, also show the plot of all entities and their movement. Show the plot for d = 30 for the best angle, and print the time. Also, write the equations governing the movement of raptors. Changing the scenario in Problem 1, we now assume that you can change your direction as well. Your run for a fixed period of time (say, dt). After this, you re-evaluate your direction to pick the best direction from that instant. You keep running in this manner. How long before you get caught? Plot the trajectories for this case for dt = 0.01s. All other parameters stay the same. Highlight changes in equations from solution to problem 1. In this problem, there is only one raptor, which is on the same line as you (say, x-axis). The raptor spots you 50 meters away and runs towards you, accelerating at 4 m/s^2 up to its maximum speed of 25 m/s. You run with an acceleration of 2 m/s^2 and your maximum speed is 8 m/s. How long before you get caught? Write a Matlab program to simulate this process. Furthermore, if the distance between you and the raptor is d meters and it takes time of t seconds before you get caught, write a mathematical expression of t in terms of the distance d
