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

Answer 1

To determine the correct function that represents the height \( h \) of the egg after \( t \) seconds when it is thrown straight up with an initial velocity, we can use the general formula for the height of an object in projectile motion, which is:

\[
h(t) = -16t^2 + vt + h_0
\]

where:
- \( -16 \) is the acceleration due to gravity (in feet per second squared),
- \( v \) is the initial velocity (in feet per second),
- \( h_0 \) is the initial height (in feet),
- \( t \) is the time in seconds.

Given the parameters from the problem:
- The initial velocity \( v = 40 \) feet per second,
- The initial height \( h_0 = 100 \) feet (the height of the building).

Substituting these values into the formula, we get:

\[
h(t) = -16t^2 + 40t + 100
\]

Therefore, the correct function representing the height \( h \) of the egg after \( t \) seconds is:

**h(t) = −16t² + 40t + 100**