Krishna
0

Step 1: Analyse the given question

            NOTE:  First ball fallen from the 120 m

                        After striking the floor ball rebounds to 0.8 * height = 0.8*120 = 96m

                       Again it fallen from the height 96m

                     Again it strikes the floo and rebounds to  0.8 * height = 0.8*96 =76.8m  

                      This process is continues till infinite    


Step 2:  Find the total distance traveled  

            Add all the values

            Total distance = 120 + 96 + 96 + 76.8 + 76.8 +............... infinite

                                  = 120 + 2(96 + 76.8,......)   ...................(1)

Step 3: Find the sum of infinite numbers in G.P

                96 + 76.8+.............. (since equation(1))

    We can write this as 96 + 96(0.8) + 96 (0.8)^2.......... In G.P

                                      a + ar + a r^2

            It is looks like in geometric progression

So, find the sum of the infinite terms  = [math] \frac{a}{1-r}[/math

                      a = fist term = 96

                      r = common ratio = 0.8

                = \frac{96}{1- 0.8}

                = 480


Step 4:  Substitute the sum of the infinite terms value in equation (1)

           Total distance = 120 + 2* (480)

                                  = 120 + 960

                                 = 1080 m