A geometric progression is a sequence of numbers where each term is found by multiplying the previous term by a constant number called the common ratio. For example, in the sequence 1, 2, 4, 8, 16, the common ratio is 2.
Geometric progression is used in ball bouncing distance calculation because the distance the ball travels with each bounce follows a geometric progression. This is because each bounce is a multiple of the previous bounce, and the common ratio is the coefficient of elasticity of the ball.
The factors that affect the ball bouncing distance include the coefficient of elasticity of the ball, the initial height from which the ball is dropped, and the surface on which the ball bounces.
The formula for ball bouncing distance can be derived by using the geometric progression formula, which is a_n = a_0 * r^n, where a_n is the nth term, a_0 is the initial term, and r is the common ratio. By setting a_n equal to the maximum distance the ball can travel and solving for n, the formula d = h * r^(n-1) can be obtained, where d is the maximum distance, h is the initial height, and r is the coefficient of elasticity.
No, the formula for ball bouncing distance is specific to spherical balls. Different shapes and sizes of balls will have different formulas for calculating their bouncing distance.