A squirrel was sitting in a tree and dropped an acorn. The height of the acorn above the ground, in feet, after t seconds can be modeled by the expression –16t2+23.What does the quantity 16t2 represent?
Question
A squirrel was sitting in a tree and dropped an acorn. The height of the acorn above the ground, in feet, after t seconds can be modeled by the expression –16t2+23.What does the quantity 16t2 represent?
Solution
The quantity 16t^2 in the expression -16t^2 + 23 represents the distance the acorn falls due to gravity over time.
Here's a step-by-step explanation:
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The expression given is a quadratic equation, which is often used to model the motion of objects under the influence of gravity.
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In this equation, 't' represents time in seconds.
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The term '16t^2' is part of the equation for the distance an object falls due to gravity, which is (1/2)gt^2, where g is the acceleration due to gravity. On Earth, g is approximately 32 feet per second per second. So, the 1/2g in the equation becomes 16 when g is 32.
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Therefore, '16t^2' represents the distance the acorn falls from the tree due to gravity after 't' seconds.
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The negative sign in front of '16t^2' indicates that the acorn is falling downwards.
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The '+23' in the equation represents the initial height of the acorn from the ground before it was dropped.
So, in conclusion, '16t^2' is the distance the acorn falls due to gravity over time.
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