Question

The distance, s, that an object falls from rest varies directly as the square of the time, t, of the fall. a book dropped from the top of a building falls 144 feet in 3 seconds. estimate the height of the building to the nearest whole number if it takes approximately 2.3 seconds for the book to hit the ground.

Answer 1

approximately 85 feet

Explanation:

Since s varies directly as the square of t, then the variation equation takes the form
`s=kt^2`.

Solve for k by substituting s=144 and t=3. That is,

`s=kt^2\\144=k(3)^2\\k=16.`

With k=16, then the variation equation is
`s=16t^2.`

To find the height, s, after 2.3 seconds, substitute t=2.3 in the equation of variation. That is,

`s=16t^2\\s=16(2.3)^2\\s=16(5.29)\\s=84.64\\s\approx85.`

Hence, the height, s, after 2.3 seconds is approximately 85 feet.