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A pebble is dropped from the edge of a tall cliff into the ocean. The pebble's height above the ocean in feet can be modeled by the expression 400–16t2, where t is the time in seconds after the pebble is released.What does the quantity 16t2 represent in the expression?

Question

A pebble is dropped from the edge of a tall cliff into the ocean. The pebble's height above the ocean in feet can be modeled by the expression 400–16t2, where t is the time in seconds after the pebble is released.What does the quantity 16t2 represent in the expression?

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Solution

The quantity 16t^2 in the expression represents the distance the pebble falls due to gravity over time t. In physics, the formula for the distance an object falls due to gravity is given by 1/2gt^2, where g is the acceleration due to gravity. On Earth, g is approximately 32 feet per second per second. So, the 16t^2 in the equation is half of 32 (which is 16) times the time squared, representing the distance the pebble falls from the cliff into the ocean over time t.

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