90.0k views
2 votes
The distance that a free falling object falls is directly proportional to the square of the time it falls (before it hits the ground). If an object fell 89ft in 2 seconds, how far will it have fallen by the end of 8 seconds? (Leave the variation constant in fraction form or round to at least 2 decimal places. Round your final answer to the nearest foot.)

User DarkAnt
by
8.1k points

1 Answer

3 votes

Given:

The object fell 89 ft.

Time is taken 2 sec.

Find:

How far in 8 sec.

Sol:

Distance, d varies directly with the square of the time, t.


\begin{gathered} d\propto t^2 \\ \\ d=kt^2 \end{gathered}

If d = 89 and t=2


\begin{gathered} d=kt^2 \\ \\ 89=k(2)^2 \\ \\ k=(89)/(4) \\ \\ k=22.25 \end{gathered}

So the equation is:


d=22.25t^2

Distance after 8 sec.


\begin{gathered} d=22.25t^2 \\ \\ d=22.25(8)^2 \\ \\ d=22.25*64 \\ \\ d=1424 \end{gathered}

So fell after 8 seconds is 1424 ft

User Choonkeat
by
8.5k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories