1. ( 10 points) 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. Specically, we assume the coordinates om), r1 and r2 are (0 ,d ), (-dJ/g d/2) and ( ME/2, zz/2), respectively. Your coordinate is (0, 0). That is, the distance between you and any of the raptors is of meters. The raptors all run towards you at different speeds with r0, II and r2 being 16 171/3, 12 m/s and 14 m/s, respectively. Your speed is 8 m/ 3. Assume that you only pick your direct ion in the beginning and stick to this direction. Find the direction that maximizes your survival time . 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 = 40 for the best angle, and print the time. Also, write the equations governing the movement of rapt ors