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You drop a water balloon from a height of 114 feet. What does the function [tex]h(t) = -16t^2 + 114[/tex] represent?

Answer :

Final answer:

The function h(t)=-16t^(2)+114 describes the height of a water balloon dropped from 114 feet over time. The -16 represents half the acceleration due to gravity in feet per second squared.

Explanation:

The function h(t)=-16t^(2)+114 is a model used in physics to describe the height of an object in free fall over a certain time period. In this case, it describes the height in feet (h) of a water balloon being dropped from an initial height of 114 feet (the number 114 being a constant in the equation), after t seconds. The number -16 is a constant representing half the acceleration due to gravity (in feet per second squared), when the direction towards the ground is chosen as negative. This equation is derived from the physics principle of motion under uniform acceleration, often represented as h(t) = ut + 0.5gt^2, where u is the initial velocity (zero if the object is dropped), g is the acceleration due to gravity, and t is time.

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