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?Choices:(A)the time in seconds it takes for the coconut to fall t feet(B)the time in seconds it takes for the coconut to reach a height of t feet(C)the distance in feet the coconut has fallen after t seconds(D)the height in feet of the coconut above the ground after t seconds
Q. 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?Choices:(A)the time in seconds it takes for the coconut to fall t feet(B)the time in seconds it takes for the coconut to reach a height of t feet(C)the distance in feet the coconut has fallen after t seconds(D)the height in feet of the coconut above the ground after t seconds
Height Expression Explanation: The expression for the coconut's height is 50−16t2. We know that the initial height is 50 feet, so the term −16t2 must represent the change in height over time.
Acceleration Due to Gravity: The term 16t2 is associated with the acceleration due to gravity, which is 32 feet per second squared, divided by 2. This is because the formula for the distance fallen under gravity is (1/2)gt2, where g is the acceleration due to gravity.
Interpretation of 16t2: So, 16t2 is half of 32t2, which means it represents the distance the coconut has fallen after t seconds, not the time it takes to fall or the height above the ground after t seconds.
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