SOLUTION: 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)calcula

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Question 1206905: 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.

Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
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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.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

           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%5E2%2A10 =  8.1 ft 
and down            8.1 ft     3rd contact



up     0.9%5E3%2A10 =  7.29 ft 
and down            7.29 ft     4th contact


ANSWER to (a) :  10+%2B+2%2A10%2A0.9+%2B+2%2A+10%2A0.9%5E2+%2B+2%2A10%2A0.9%5E3 = 58.78 ft.



           P a r t  (b)


Calculate the sum 

     10 + 2%2A10%2A0.9+%2B+2%2A10%2A0.9%5E2+%2B+2%2A10%2A0.9%5E3+%2B+2%2A10%2A0.9%5E3+%2B+ellipsis = 10 + 2%2A10%2A0.9%281%2B0.9%2B0.9%5E2%2B0.9%5E3%2B+ellipsis%29) = 

   = use the formula of the sum of an infinite GP = 10 + 2%2A10%2A0.9%2A%281%2F%281-0.9%29%29 = 10 + 2%2A10%2A0.9%2A%281%2F0.1%29 = 10 + 20*9 = 10 + 180 = 190 ft.


ANSWER to (b) :  190 ft.

Solved.