Question

A book falls from a shelf that is 5 feet above the floor. A model for the height h in feet if an object dropped from an initial height of h₀ feet is h=-16t² + h₀, where t is the time in seconds after the object is dropped. Use this model to determine approximately how long it took for the book to reach the ground.

Answer 1

About 0.559 seconds

Explanation:

The height equation is:

`h=-16t^2+h_0`

Where
`h_0` is the initial height of the book, which is 5, so we can write:

`h=-16t^2+5`

Now, we want time it took for the book to reach ground (h = 0)

So, we substitute h = 0 and solve for t:

`h=-16t^2+5\\0=-16t^2+5\\16t^2=5\\t^2=0.3125\\t=0.5590\\t=0.559`

It took about 0.559 seconds for the book to reach the ground