A ball bounces 0.7 of the distance it is dropped. How many bounces will the ball make from a height of 1 meter if a bounce of less than 1 centimeter is to be ignored?
consider the first term to be
.7(1) = .7
term 2 = .7^2 = .49
what term = .01
.7^n = .01
n ln .7 = ln .01
n = ln.01/ln.7 = 12.9
term 12 = .7^12 = .0138 > .01
term 13 = .7^13 = .00968 < .01
To determine the number of bounces the ball will make, we need to calculate the distance covered with each bounce until it becomes less than 1 centimeter.
Let's say the ball is dropped from a height of 1 meter (which equals 100 centimeters). According to the given information, the ball bounces 0.7 of the distance it is dropped.
For the first bounce, the ball reaches a height of 0.7 * 100 = 70 centimeters.
For the second bounce, the ball reaches a height of 0.7 * 70 = 49 centimeters.
For the third bounce, the ball reaches a height of 0.7 * 49 = 34.3 centimeters.
We continue this process until the height of the bounce becomes less than 1 centimeter.
So, the number of bounces the ball will make is determined by dividing the initial drop height by the minimum bounce height.
Number of bounces = (initial drop height) / (minimum bounce height)
Number of bounces = 100 centimeters / 1 centimeter
Therefore, the ball will make 100 bounces from a height of 1 meter if a bounce of less than 1 centimeter is ignored.