Inelastic Bouncing Ball Background We leam in introductory physics that when an object is dropped from rest its potential graviational energy (PE) is converted into kinefic energy (KE). If there is no friction (i.e_, drag) between the object and the air (or water, or whatever the surreunding environment is composed of) then conservation of energy tells us that the change in the object's PE is equal to its change in KE: APE = AKE In terms of relevant physical variables, this relationship is written as mgih h) == m(V3V]) where m is the object's mass, g is the (constant) acceleration due to gravity, h is the object's height above some reference point, V is the object's velocity, and the subscripts 1 and 2 represent the initial and final states of the object. respectively. This classic falling object problem is often used to answer questions like, "What is the object's velocity right before it hits the ground?\" Once we have a grasp of these simple falling object problems, it is interesting to fry to answer new guestions like, "What happens after the object hits the ground?\" This question naturally leads to the study of collisions. For perfectly elastic collisions, no energy is lost and the upward velocity of the ball just after it hits the ground is exactly equal to the downward velocity of the ball just before it hits the ground. In this idealized scenario the ball will bounce all the way back up to its initial height (m) and confinue deing so forever; clearly, the elastic collision case does nof describe real collisions. A more realistic mathematical model for a bouncing object leads us to the study of inelastic collisions. For inelastic collisions, the upward velocity of the object after rebounding off the ground is less than its downward velocity just before striking the ground. The ratio of the magnitudes of these velocities is called the coefficient of restitution () velocity after striking ground| = Tvelocity before striking ground] - Elastic collisions are described by = | and inelastic collisions are described by 0 = 1 4 error('coefficient of restitution must have an absclute value less than 1.'); 5 end 6 % Calculate total distance traveled 7 Totalpist = hl * (1 + e~2) / (1 - e~2); 8 9 % Calculate number of bounces required to cover at least 35% of total distance 18 Bounceout = ceil(log(@.e5) / log(e~2)); 1 12 % Calculate distance vector 13 7 = zeros(1, BounceDut+1); 1 for 1 = 1:Bouncedut 15 (i) = 2 * h1 * e~(2%(i-1}); 16 17 end 18 z_total_distance = Totalbist; 19 [ end 28 Code to call your function @ 1|hl =1; 2le = 8.7; 3 | [TotalDist,Bounceout,z] = BallBounce({hl,e} Assessment: 2 of 3 Tests Passed (78%) & Check total distance calculation. 1% (11%) & Check number of bounces calculation. 67% (67%) & Check distance as a function of number of bounces. 0% (22%) Variable z has an incorrect value. Make sure your cufput here is a vector. Also make sure the last element of the vector is the distance traveled for the number of bounces that satisfies the minimum distance traveled condiion. Total