A Ball Bounces 8 Times Find Distance Travelled Geometri Watch?v=kmprzz4nttc pendulum infinite series: watch?v=43wyibmbnoi&list=plj ma5djyaqoulou8yurv0 swvzuoqff8&ind. This lesson explains the good old bouncing ball problem. it explains how to use geometric series to find the total distance of the bouncing ball.
Infinite Geometric Series Bouncing Ball Youtube Determining the total distance of a bouncing ball. The corresponding series can be written as the sum of the two infinite geometric series: one series that represents the distance the ball travels when falling and one series that represents the distance the ball travels when bouncing back up. series 1 5 3.25 2.1125 ⋯ series 2 3.25 2.1125 1.373125 ⋯ find the sum of each series. Here is a method which avoids summing a geometric progression (at least it hides a method for computing the sum). call the height of the table h = 4a h = 4 a and the total distance travelled d d. to the top of the first bounce the ball travels down 4a 4 a and back up 3a 3 a. the remainder of the track of the ball is exactly as if it had fallen. Jan 19, 2009. #1. a bouncing balls reaches heights of 16 cm, 12.8 cm and 10.24 cm on three consecutive bounces. a) if the ball started at a height of 25 cm, how many times has it bounced when it reaches a height of 16 cm? b) write a geometric series for the downward distances the ball travels from its release at 25 cm.
Precalculus Geometric Series Bouncing Ball Distance Traveled Series Here is a method which avoids summing a geometric progression (at least it hides a method for computing the sum). call the height of the table h = 4a h = 4 a and the total distance travelled d d. to the top of the first bounce the ball travels down 4a 4 a and back up 3a 3 a. the remainder of the track of the ball is exactly as if it had fallen. Jan 19, 2009. #1. a bouncing balls reaches heights of 16 cm, 12.8 cm and 10.24 cm on three consecutive bounces. a) if the ball started at a height of 25 cm, how many times has it bounced when it reaches a height of 16 cm? b) write a geometric series for the downward distances the ball travels from its release at 25 cm. In this video we use a geometric sequence to determine how high a ball is bouncing and an infinite geometric series to determine the total vertical distance. (b) find the number of times, after the first bounce, that the maximum height reached is greater than 10cm. (c) find the total vertical distance travelled by the ball from the point at which it is dropped until the fourth bounce. answer explanation. ans: (a) use of geometric sequence with r = 0.85 either \((0.85)^6(1.8)\) or 0.678869….
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