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

Answer 1

To determine the height \( h(t) \) of the egg after \( t \) seconds, we can use the following kinematic equation for an object projected upward:

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

where:
- \( -16t^2 \) represents the effect of gravity (assuming the acceleration due to gravity is \( -32 \) feet per second squared, which is divided by 2),
- \( v_0 \) is the initial velocity in feet per second,
- \( h_0 \) is the initial height from which the egg is thrown.

In this scenario:
- The initial velocity \( v_0 \) is \( 40 \) feet per second.
- The initial height \( h_0 \) from which the egg is thrown is \( 100 \) feet.

Plugging these values into our equation, we have:

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

So the correct function representing the height of the egg after \( t \) seconds is:

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