math
posted by Marisol .
A ball has a 75% rebound ratio. When you drop it from a height of 16 ft, it bounces and bounces...
When it strikes the ground for the second time, the ball has traveled a total of 28 ft in a downward direction. How far downward has the ball traveled when it strikes the ground for the 17th time?

T(1)=16
T(2)=12
T(3)=9
...
T(n)=16(3/4)^(n1)
It is a geometric progression (GP) with a ratio of 3/4.
The sum to n terms of a GP is:
S(n)=16(1(3/4)^n)/(1(3/4))
Substitute n=17 in the above formula to get S(17), the total downward distance.
Respond to this Question
Similar Questions

math
a ball is dropped from a height of 5m. after each bounce, the ball rises to 45% of its previous height. what the total vertical distance that the ball has travelled after it has hit the ground for for the 6th time? 
math
the height that a ball bounces varies directly as the height from which it is dropped. A ball dropped from a height of 20cm bounces 16cm a) Find the height of the bounce if the ball is dropped from a height of 280cm b) Find from waht … 
math
a ball is dropped from a height of 3m and bounces on the ground . At the top of each bounce, the ball eaches 60% of its previous height. Calculate the total distance travelled by the ball when it hits the ground for the fifth time 
physics
A ball is tossed so that it bounces off the ground, rises to a height of 0.90 m, and then hits the ground again 0.50 m away from the first bounce. How long is the ball in the air between the two bounces? 
physics
A ball is tossed so that it bounces off the ground, rises to height of 2 m, and then hits the ground again 0.75 m away from the first bounce. a. How long is the ball in the air between the two bounces? 
Physics
The Colliding Balls: A ball is released from rest at a height h above the ground. The ball collides with the ground and bounces up at 75% of the impact speed the ball had with the ground. The collision with the ground is nearly instantaneously. … 
algebra
When a tennis ball is dropped, it rebounds to 70% of its initial height. If we drop a tennis ball from 10 ft, determine the total distance traveled by the ball after 10 bounces. 
math
a student drop a rubber ball from a height of 8 feet . Each time the ball hits the ground, it bounces to 75% of its previous height. a/ how far does the ball travel between tne second and third bounces . b/ write an infinite series … 
physics
A ball dropped from a sixth floor window accelerates at 10 m/s After 2 seconds it hits the ground. It bounces back with a velocity of 15 m/s. What is the ballâ€™s velocity when it hits the ground? 
Algebra 2
A ball is dropped from a height of 25 feet and allowed to continue to bounce until it eventually comes to a rest. Each time the ball bounces it rebounds to 45 of its previous height. After which bounce is the ball's rebound height …