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 +100t −40
h(t) = −16t2 +100t −40

h(t) = −16t2 −40t−100
h(t) = −16t2 −40t−100

h(t) = −16t2 −100t + 40
h(t) = −16t2 −100t + 40

h(t) = −16t2 + 40t + 100
h(t) = −16t2 + 40t + 100

Answer 1

To determine the function that represents the height \( h \) of the egg after \( t \) seconds when it is thrown straight up from the top of a 100-foot building with an initial upward velocity of 40 feet per second, we can use the general equation for the motion of an object under the influence of gravity, which is:

\[
h(t) = -16t^2 + v_0 t + h_0
\]

where:
- \( -16t^2 \) represents the effect of gravity (in feet),
- \( v_0 \) is the initial velocity (in feet per second),
- \( h_0 \) is the initial height (in feet).

In this problem:
- The initial velocity \( v_0 = 40 \) feet/second,
- The initial height \( h_0 = 100 \) feet.

By substituting these values into the equation, we have:

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

Thus, the correct function that represents the height of the egg after \( t \) seconds is:

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