A ball is dropped from 5m of height with no initial speed. With each bounce, the ball reaches 3/4 of the last height. Please theoretically find the total distance of the ball

SOLUTION For this problem, we can solve for the total distance the ball travelled using sum of infinite geometric progression. The formula is: $$ S=\frac{a_1}{1-r} $$ where S is the sum, a1 is the first term, and r is the geometric ratio For this problem, we are asked to solve for S, given the value of a1 to be 5 and r to be 3/4. Substituting the values into the formula, we'll get: $$ S=\frac{a_{1}}{1-r} $$ $$ S=\frac{5}{1-\frac{3}{4}} $$ $$ S=\frac{5}{\frac{1}{4}} $$ $$ S=\frac{5\times4}{1} $$ $$ S=20 $$ ANSWER: 20 meters