Question

A Bungee Jumper Falls 97.2 Feet Before Bouncing Back Up At The End Of His Bungee Cord. Then He Falls 64.8 Feet Before Bouncing Up Again. On His Third Descent, He Falls 43.2 Feet Before Going Back Up. What Is The Total Distance The Bungee Jumper Drops After Five Falls If The Distances Continue In This Pattern? (Do Not Include The Distance Traveled Up.)

Answer 1

Answer:

253.2 ft

Step-by-step explanation:

A Bungee Jumper Falls 97.2 Feet Before Bouncing Back Up At The End Of His Bungee Cord. Then He Falls 64.8 Feet Before Bouncing Up Again. On His Third Descent, He Falls 43.2 Feet Before Going Back Up. What Is The Total Distance The Bungee Jumper Drops After Five Falls If The Distances Continue In This Pattern

First Distance = 97.2 ft

Second distance = 64.8 ft

Third distance = 43.2 ft

64.8/97.2 = 2/3    & 43.2/64.8 = 2/3

r = common ration = 2/3

This is an Gp

where a = 97.2  ft   & r = 2/3

Sum for 5 terms  = a (1 - rⁿ)/(1 - r)     ( as r < 1)

= 97.2  ( 1 - (2/3)⁵)/(1 - 2/3)

= 97.2 (1 - 32/243)/(1/3)

= 97.2(211)/81

= 253.2 ft

or simply 4th distance = 43.2 * 2/3 = 28.8 ft

& 5th Distance = 28.8 * 2/3 = 19.2 ft

Total Distance Dropped = 97.2 + 64.8 + 43.2 + 28.8 + 19.2 =   253.2