# CS project 1

4.uising mat lab code The rabbit isn’t trying to outrun Diesel, it’s just trying to run long enough for Diesel to give up. So, let’s call the chase concluded when/if 􏰀(xR(t) − xD(t))2 + (yR(t) − yD(t))2 < .1 or t > 6 (Diesel can’t run for more than 6 seconds) Let’s see when Diesel actually catches the rabbit.

(a) (5 points) Write the IVP for Diesel’s position using the definition of the rabbit’s velocity and the initial conditions from above.

(b) (20 points) Code Euler’s Method to calculate an approximate solution to the IVP using the initial values and velocities discussed above. Run Euler’s method for CR = CD = 1 and x0 = 1 to find if Diesel catches the rabbit. If he does, when does he catch the rabbit? If not, how close does he get at t = 6? Generate a plot of the distance between Diesel and the rabbit as a function of time.

(c) (10 points) Now, suppose the rabbit makes another turn of 90 degrees to the left at a fix rate of 45 degrees/second starting at t = 3. Repeat the above with this addition. Answer the same questions. Generate the same plot.

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