Q. A basketball is dropped from a height of 40 feet.it bounces back each time to a height which is one half of the height of the last bounce.how far approximatesly will the ball have to be travelled before it comes to rest?
Option
A)80FT.
b)120 ft
C)180 ft
d)CANNOT B DETERMINED

• ist time ball travels 40 ft before striking, after that it goes 20 ft up & comes back 20 ft down, then 10 ft up & 10 ft down etc
  
  assume that the ball comes to rest at infinity
  
  total distance travelled before coming to rest = 40+(20+20)+(10+10)+(5+5)+(2.5+ 2.5)+ ... upto infinity
  
  = 40 + 2*(20+10+5+2.5+ ...)
  = 40 + 2*[20/(1- 1/2)] [sum of infinite GP = a/(1-r)]
  = 20 + 80
  = 120 ft
  b)120 ft
• 10 years agoHelpfull: Yes(82) No(1)
• 40+2[40/2+40/4+40/8...] (2 is defined because of the bounce)
  40+2*40[1/2+1/4+1/8...] (1/2+1/4+1/8..= 1=> first term / 1-difference between the terms )
  40+2*40[1]
  120 feet
• 10 years agoHelpfull: Yes(11) No(0)
• This is a GP question...
  first ball travels 40ft while going down....
  then it bounce back to 20ft and comes down again travelling 20ft..
  again it bounce back to 10ft and comes down travelling 10ft..
  again it bounce back 5ft and comes down travelling 5ft...
  so sum will be like 40+20+20+10+10+5+5.......up to infinity
  or it can be seen as (40+20)+(20+10)+(10+5)+........=60+30+15+...........
  this is an infinite series with a=60 and r=30/60=1/2
  so sum of infinite series is given by,
  a/(1-r)=60/(1-1/2)=120ft
  so ANS: 120ft
• 9 years agoHelpfull: Yes(2) No(0)
• ok ok... sorry.... i understand.... thanks for giving us solution
• 10 years agoHelpfull: Yes(1) No(1)
• 40/(1-(1/2)) (+) 20/(1-(1/2)) =120
  check for all these kind of prob & the decrement of the distance travelled sud be taken carefully n thus u cn find the solution
• 10 years agoHelpfull: Yes(1) No(1)
• how can dis possible that 20+80=120??? plz xplain rakesh
  thanks..
• 10 years agoHelpfull: Yes(0) No(2)
• 40+40+20+10+5+2.5+1.25+0.625+..........
  =120ft
• 8 years agoHelpfull: Yes(0) No(1)
• A) 80 ft
  
  s=a/(1-r) where s is sum, a is 1st term and r is common ratio
• 8 years agoHelpfull: Yes(0) No(0)
• train travel from a to b then b to a then a to half of distance from b
  so... total dist.= 27+27+(27/2)=67.5km
  relative speed= 5+7= 12 km/h (as direction is opposite)
  thus, 67.5/12= 5.62hrs
  so 01:05
• 8 years agoHelpfull: Yes(0) No(0)