Question

Math 2510 Take Home 1 4. Collisions. Consider two particles following the two planar paths r()= (sin (2r), cos (t) r,(f)(sin (t),cos (21) Notice, r(0) =(0,1)=r, (t) so the particles start at the same point. a) At how many points in the plane do their paths cross? Make a rough sketch showing the intersections. tl lon b) Find the first positive time of a collision. c) Use the velocity vectors to describe what happens at the time of the first collision Page 5 of 8

please explain this in detail step by step for better understanding. Thank you!

Answer 1

4. Collisions.Consider two particles following the two planar paths 5()=(sin (21).cos()) r, (t)(sin (t),cos (2r). a) At how many points in the plane do their paths cross? Make a rough sketch showing the intersections 1:5t プhe slatch of the rofhis (0, 1) for tha two paRy 0-5 me hore (0.588, 0.309) (-0.588, 0.309) Co,1) amol -15 1.5 -0.5 0.5 (0.866, -0.5) (0.866, -0.5) Starng pusnt Hore -0.5 (0.951,-0.809) (- -0.809) In totbl ,thene are 7 points af irorseeono shswn n aouve b) Find the first positive time of a collision. The Bat colliston cccurs at x0.588 Y0,039 wich s t 2n/ seconals c) Use the velocity vectors to describe what happens at the time of the first collision. Drfferemtsngfoson veets get the velociy FL4)0 C2 scat),-sin t) t Cent, -2sn(at ita rarpeat t,we veetra as amd と) =(-.618,-0.951) t0.s09,-h17 4), CAt Hfat calli sie nd