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
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16t2+23.
What does the quantity 16t2 represent?
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16t2+23.
What does the quantity 16t2 represent?
Answers
GPT-4o mini
In the expression for the height of the acorn above the ground, \( h(t) = -16t^2 + 23 \), the term \(-16t^2\) represents the effect of gravity on the acorn's motion.
The value 16 is derived from the standard equation of motion for objects under the influence of gravity near the Earth's surface, where acceleration due to gravity is approximately \(32 \, \text{ft/s}^2\). The negative sign indicates that gravity acts downward, causing the height to decrease over time. The \(t^2\) factor indicates that the distance fallen is proportional to the square of the time, which is a typical characteristic of uniformly accelerated motion.
Thus, the quantity \(16t^2\) specifically represents the distance (in feet) that the acorn falls due to the force of gravity after \(t\) seconds.
The value 16 is derived from the standard equation of motion for objects under the influence of gravity near the Earth's surface, where acceleration due to gravity is approximately \(32 \, \text{ft/s}^2\). The negative sign indicates that gravity acts downward, causing the height to decrease over time. The \(t^2\) factor indicates that the distance fallen is proportional to the square of the time, which is a typical characteristic of uniformly accelerated motion.
Thus, the quantity \(16t^2\) specifically represents the distance (in feet) that the acorn falls due to the force of gravity after \(t\) seconds.