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A coconut falls from the top of a tall palm tree. The coconut's height above the ground in feet can be modeled by the expression 50–16t2, where t is the time in seconds after the coconut begins to fall.What does the quantity 16t2 represent in the expression?

Question

A coconut falls from the top of a tall palm tree. The coconut's height above the ground in feet can be modeled by the expression 50–16t2, where t is the time in seconds after the coconut begins to fall.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 coconut has fallen from its original height due to gravity. In physics, the formula to calculate the distance an object falls due to gravity is 1/2gt^2, where g is the acceleration due to gravity. On Earth, g is approximately 32 feet per second squared. In the expression 50-16t^2, the 16t^2 is half of 32t^2, which means it's representing the distance the coconut has fallen over time t.

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