Question
You are tossing an egg from the top of a building that is 100 feet above the ground. The egg will be thrown straight up at a velocity of 40 feet per second. Which function below represents the height h of the egg after t seconds? (1 point)
Responses
h(t) = −16t2 −40t−100
h(t) = −16t2 −40t−100
h(t) = −16t2 −100t + 40
h(t) = −16t2 −100t + 40
h(t) = −16t2 +100t −40
h(t) = −16t2 +100t −40
h(t) = −16t2 + 40t + 100
Responses
h(t) = −16t2 −40t−100
h(t) = −16t2 −40t−100
h(t) = −16t2 −100t + 40
h(t) = −16t2 −100t + 40
h(t) = −16t2 +100t −40
h(t) = −16t2 +100t −40
h(t) = −16t2 + 40t + 100
Answers
GPT-4o mini
To determine the correct function representing the height \( h \) of the egg after \( t \) seconds, we can use the general formula for projectile motion:
\[
h(t) = -16t^2 + vt + h_0
\]
where:
- \( -16t^2 \) accounts for the acceleration due to gravity (in feet per second squared),
- \( v \) is the initial velocity,
- \( h_0 \) is the initial height.
In this case:
- The initial velocity \( v = 40 \) feet per second (upward),
- The initial height \( h_0 = 100 \) feet (the height of the building).
Plugging these values into the formula gives us:
\[
h(t) = -16t^2 + 40t + 100
\]
Thus, the correct function that represents the height \( h \) of the egg after \( t \) seconds is:
\[
h(t) = -16t^2 + 40t + 100
\]
So the answer is:
**h(t) = −16t² + 40t + 100**
\[
h(t) = -16t^2 + vt + h_0
\]
where:
- \( -16t^2 \) accounts for the acceleration due to gravity (in feet per second squared),
- \( v \) is the initial velocity,
- \( h_0 \) is the initial height.
In this case:
- The initial velocity \( v = 40 \) feet per second (upward),
- The initial height \( h_0 = 100 \) feet (the height of the building).
Plugging these values into the formula gives us:
\[
h(t) = -16t^2 + 40t + 100
\]
Thus, the correct function that represents the height \( h \) of the egg after \( t \) seconds is:
\[
h(t) = -16t^2 + 40t + 100
\]
So the answer is:
**h(t) = −16t² + 40t + 100**