Question

When a ball falls from an initial height h, its speed s when it reaches the floor is given by the relation: s = squareroot 2 *h *g where g is the gravity constant 9.81 Immediately after hitting the floor, its speed becomes s1 = eps*s (where eps is a constant and s its speed before rebounding). The ball will then reach the height h1 = (s1)^2/(2*g) = (s*eps)/(2*g). After n rebounds, what is the equation of the height reached by the ball? Write a program (rebounding epp) that computes the height reached the ball after rebound 1, 2, ..., n rebounds. Print a statement before the height reached. Your program should define the constant g Your program should request from the user h0 (the initial height) eps (the rebound coefficient, 0 < eps < 1) n (the number of rebounds, 0 <= n) For h0 = 25, eps = 0.9, and n = 10, the height obtained should be around 3.04 To use squareroot () function you will need to # include <c math>

Answer 1

rebounding.cpp

#include <bits/stdc++.h>
#include <math.h>
using namespace std;

int main()
{
   float h,e;
   float g = 9.8;
   int n;
   cout << "Enter initial height h in meters\n";
   cin >> h;
   cout << "Enter Coefficient of restitution\n";
   cin >> e;
   cout << "Enter number of rounds n\n";
   cin >> n;
   int i = 1;

   while(i<=n)
   {
       float s = sqrt(2*g*h);
       h = (e*s)*(e*s)/(2*g);
       cout << "After " << i << " Rebounds, height reached by ball: " << h << endl ;
       i++;
   }
   return 0;
}

Sample Output:

Enter initial height h in meters
25
Enter Coefficient of restitution
0.9
Enter number of rounds n
10
After 1 Rebounds, height reached by ball: 20.25
After 2 Rebounds, height reached by ball: 16.4025
After 3 Rebounds, height reached by ball: 13.286
After 4 Rebounds, height reached by ball: 10.7617
After 5 Rebounds, height reached by ball: 8.71696
After 6 Rebounds, height reached by ball: 7.06074
After 7 Rebounds, height reached by ball: 5.7192
After 8 Rebounds, height reached by ball: 4.63255
After 9 Rebounds, height reached by ball: 3.75236
After 10 Rebounds, height reached by ball: 3.03942