The function \( h(t) = -16t^2 + 55t \) represents the height of a ball thrown into the air based on time \( t \). The question seems to ask for the interpretation of a specific moment in relation to this function.
To find the correct interpretation, we can analyze the provided responses:
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The ball hits the ground after 3 seconds: This would be true if \( h(t) = 0 \) at \( t = 3 \), but to confirm that, we would need to set the height equation equal to zero and solve for \( t \).
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The time it takes to reach the maximum point is 3 seconds: The maximum height can be found at \( t = -\frac{b}{2a} \), where \( a \) and \( b \) are coefficients from the quadratic equation \( at^2 + bt + c \). For this equation, \( a = -16 \) and \( b = 55 \). Using this formula, we would calculate to confirm this assertion.
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The height of the ball 3 seconds after it has been thrown: This directly represents \( h(3) \), which can be calculated to find the height at 3 seconds.
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The time it takes the ball to be 3 ft up in the air: This would involve solving the equation \( h(t) = 3 \) for \( t \), which would give the time(s) at which the ball is at that height.
To clarify which of these options is correct, it's necessary to either calculate the respective values or analyze the context given. If we specifically refer to what “3” represents in a general context, without solving the values, your interpretation may depend primarily on that specified context.
In standard situations, the correct interpretation may often be the height at a specific time or when it reaches maximum height, rather than hitting the ground without additional computation.
Therefore:
- If the question asks how we interpret \( t = 3 \) in general for this function, the best option would be "The height of the ball 3 seconds after it has been thrown."
If you need specifics or calculations for any of the options provided, please let me know!