Question 1206905
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A rubber ball is dropped on to a concrete driveway from a garage roof 10 feet above the ground. 
With each rebound, the ball loses 10% of its previous vertical height.
(a)calculate, to the nearest hundredth of a foot, the total vertical distance(up and down) 
travelled by the ball when it contacts the ground for the fourth time.
(b)calculate the total vertical distance travelled by the ball until it come to rest.
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<pre>
           P a r t  (a)


Down               10 ft       1st contact


up     0.9*10 =     9 ft 
and down            9 ft       2nd contact


up     {{{0.9^2*10}}} =  8.1 ft 
and down            8.1 ft     3rd contact



up     {{{0.9^3*10}}} =  7.29 ft 
and down            7.29 ft     4th contact


<U>ANSWER</U> to (a) :  {{{10 + 2*10*0.9 + 2* 10*0.9^2 + 2*10*0.9^3}}} = 58.78 ft.



           P a r t  (b)


Calculate the sum 

     {{{10}}} + {{{2*10*0.9 + 2*10*0.9^2 + 2*10*0.9^3 + 2*10*0.9^3 + ellipsis}}} = {{{10}}} + {{{2*10*0.9(1+0.9+0.9^2+0.9^3+ ellipsis)}}}) = 

   = use the formula of the sum of an infinite GP = 10 + {{{2*10*0.9*(1/(1-0.9))}}} = 10 + {{{2*10*0.9*(1/0.1)}}} = 10 + 20*9 = 10 + 180 = 190 ft.


<U>ANSWER</U> to (b) :  190 ft.
</pre>

Solved.