Question
h(t) = −16t2 + 80t + 30
Does it make sense to find h(−10) in the context of this problem?
Does it make sense to find h(−10) in the context of this problem?
Answers
Answered by
GPT-4o mini
The function \( h(t) = -16t^2 + 80t + 30 \) models the height of an object (such as a projectile) over time \( t \) in seconds. The context of the function is likely related to motion under the influence of gravity, which is encapsulated by the term \(-16t^2\) (indicating a downward acceleration due to gravity, with \( -16 \) representing half of the acceleration in feet per second squared).
When considering whether it makes sense to evaluate \( h(-10) \), we need to think about what negative time (\( t < 0 \)) would represent in the context of this problem:
1. **Physical Interpretation**: In typical projectile motion problems, time \( t \) represents the time elapsed since the object was launched. Negative time would imply a time before the launch, which doesn't have a physical meaning in this context.
2. **Mathematical Evaluation**: While the function can be evaluated mathematically for \( t = -10 \), yielding a height value, the result does not correspond to any real-world scenario in terms of the object's flight.
In conclusion, it does not make sense to find \( h(-10) \) in the context of this problem, as negative time does not correspond to a meaningful physical situation related to the object's motion.
When considering whether it makes sense to evaluate \( h(-10) \), we need to think about what negative time (\( t < 0 \)) would represent in the context of this problem:
1. **Physical Interpretation**: In typical projectile motion problems, time \( t \) represents the time elapsed since the object was launched. Negative time would imply a time before the launch, which doesn't have a physical meaning in this context.
2. **Mathematical Evaluation**: While the function can be evaluated mathematically for \( t = -10 \), yielding a height value, the result does not correspond to any real-world scenario in terms of the object's flight.
In conclusion, it does not make sense to find \( h(-10) \) in the context of this problem, as negative time does not correspond to a meaningful physical situation related to the object's motion.