A rubber ball dropped on a hard surface takes a sequence of bounces, each one 3/5 as high as the preceding one. If this ball is dropped from a height of 10 feet, what is the total vertical distance it has traveled after it hits the surface the 5th time?

Question

parthkohli · Answer

Add this 10 + 10(3/5) + 10(3/5)^2 + 10(3/5)^3 + 10(3/5)^4 + 10(3/5)^5

anonymous · Answer

@ParthKohli dont got my calc on me :/

parthkohli · Answer

Use your brain then :D

parthkohli · Answer

Or use wolfram..

campbell_st · Answer

there are 2 series here.... 

the down series where  a = 10 and r = 3/5   and n = 5

the up series where a = 6 and r = 3/5  and n = 4 as after bouncing the ball only goes up 4 times

this is a geometric series where r < 1

so use

$$s _{n}= \frac {a(1 - r^n)}{1 - r}$$

$$s _{5}= \frac{10(1 - (\frac{3}{5})^5)}{1 - \frac{3}{5}} + \frac{6(1 - (\frac{3}{5})^4}{1 - \frac{3}{5}}$$

just evaluate it