A Ball Is Dropped from a Height of 10 Feet

question 15

Short Answer

A ball is dropped from a height of 10 feet and bounces. Each bounce is 2/3 the height of the bounce before. Find an expression for the height to which the ball rises after it hits the floor for the n^th time, and use it to find the total vertical distance the ball has traveled when it hits the floor for the 4^th time. Round to 2 decimal places.

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Definitions:

System-2 Thinking

Reflective critical thinking that is useful for judgments in unfamiliar situations, for processing abstract concepts, and for deliberating when there is time for planning and more comprehensive consideration.

Comprehensive Consideration

A thorough and all-encompassing approach to analyzing or thinking about a problem, situation, or decision.

Reflective Critical

The process of critically assessing one's beliefs, judgments, and practices through introspection and consideration of external inputs.

Salient Memories

Vivid and prominent memories that stand out due to their significance or emotional impact.