a box falls off a warehouse shelf from a height of 16 feet. the function h(t)=-16t to the power of 2 + 16 gives the height (in feet) of the box after t seconds. when does the box hit the floor

The function for the height \( h(t) \) of the box after \( t \) seconds is:

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

To find when the box hits the floor, we need to determine when the height \( h(t) \) becomes zero (since the box is on the floor at this point):

\[
-16t^2 + 16 = 0
\]

Solving this equation:

1. Subtract 16 from both sides:
\[
-16t^2 = -16
\]

2. Divide both sides by -16:
\[
t^2 = 1
\]

3. Take the square root of both sides:
\[
t = 1 \, \text{or} \, t = -1
\]

Since time \( t \) must be positive, \( t = 1 \) second.

Thus, the box hits the floor after 1 second.

Would you like further explanation on any part of this solution? Here are 5 related questions to expand your understanding:

1. How would the height function change if the box fell from a greater height?
2. What would the height function be if gravity were different on another planet?
3. How would we solve this problem using graphical methods?
4. What would happen if air resistance were factored into the height function?
5. How can we use derivatives to analyze the motion of the box?

**Tip:** Quadratic functions like this one can be solved by factoring, completing the square, or using the quadratic formula. Each method can offer different insights into the problem.

A box falls off a warehouse shelf from a height of 16 feet. The function h(t) = -16t^2 + 16 gives the height (in feet) of the box after t seconds. When does the box hit the floor?

Discover how to calculate when a box falling from a height of 16 feet hits the floor using the quadratic equation h(t) = -16t^2 + 16. Learn the steps to solve this problem, including applying the quadratic formula. Ideal for students in Grades 8-10.

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