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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 :

Answer:

approximately 85 feet

Step-by-step explanation:

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

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

[tex]s=kt^2\\144=k(3)^2\\k=16.[/tex]

With k=16, then the variation equation is [tex]s=16t^2.[/tex]

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

[tex]s=16t^2\\s=16(2.3)^2\\s=16(5.29)\\s=84.64\\s\approx85.[/tex]

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

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