Question
h(t) = −16t2 + 80t + 30
What does h(2.5) represent in the context of this problem?
What does h(2.5) represent in the context of this problem?
Answers
Answered by
GPT-4o mini
The function \( h(t) = -16t^2 + 80t + 30 \) typically represents the height of an object (like a projectile) at time \( t \), where \( h(t) \) is the height in units such as feet, and \( t \) is the time in seconds.
To find \( h(2.5) \), you would substitute \( t = 2.5 \) into the function:
\[
h(2.5) = -16(2.5)^2 + 80(2.5) + 30
\]
Calculating this:
1. Calculate \( (2.5)^2 = 6.25 \).
2. Then calculate \( -16(6.25) = -100 \).
3. Next, calculate \( 80(2.5) = 200 \).
4. Now, sum them up with the constant: \( -100 + 200 + 30 = 130 \).
So, \( h(2.5) = 130 \).
In this context, \( h(2.5) = 130 \) represents the height of the object at \( t = 2.5 \) seconds. Thus, at 2.5 seconds after launch, the object is at a height of 130 units (likely feet if this is a physics problem related to projectile motion).
To find \( h(2.5) \), you would substitute \( t = 2.5 \) into the function:
\[
h(2.5) = -16(2.5)^2 + 80(2.5) + 30
\]
Calculating this:
1. Calculate \( (2.5)^2 = 6.25 \).
2. Then calculate \( -16(6.25) = -100 \).
3. Next, calculate \( 80(2.5) = 200 \).
4. Now, sum them up with the constant: \( -100 + 200 + 30 = 130 \).
So, \( h(2.5) = 130 \).
In this context, \( h(2.5) = 130 \) represents the height of the object at \( t = 2.5 \) seconds. Thus, at 2.5 seconds after launch, the object is at a height of 130 units (likely feet if this is a physics problem related to projectile motion).