A ball is thrown vertically upward a distance of 54 meters. After hitting the ground, it rebounds 2/3 the distance fallen and continues to rebound in the same manner. What is the total distance that the ball has traveled when it hits the ground the third time? (Remember that the ball travels up a given distance, travels down the same distance, hits the ground, and then rebounds 2/3 of the previous distance.)
a) 228 meters

b) 114 meters

c) 180 meters

d) None of these

Question

A ball is thrown vertically upward a distance of 54 meters. After hitting the ground, it rebounds 2/3  the distance fallen and continues to rebound in the same manner. What is the total distance that the ball has traveled when it hits the ground the third time? (Remember that the ball travels up a given distance, travels down the same distance, hits the ground, and then rebounds  2/3 of the previous distance.)
a) 	228 meters
	
b) 	114 meters
	
c) 	180 meters
	
d) 	None of these

kainui · Answer

I suggest drawing it out, then labelling all the paths and adding them up. I can help point you in the right direction.

anonymous · Answer

Okay

zzr0ck3r · Answer

54+54+(2/3)54+(2/3)54+(2/3)(2/3)54+(2/3)(2/3)54

zzr0ck3r · Answer

54 for the first time up, 54 for the first time down
(2/3)54 for the second time up (2/3)54 for the second time down
(2/3)(2/3)54 for the third time up, (2/3)(2/3)54 for the third time down

anonymous · Answer

228?

zzr0ck3r · Answer

that's what I got

anonymous · Answer

Awesome, thank you

zzr0ck3r · Answer

$$108\sum_{n=0}^{2}(\frac{2}{3})^n$$