# A.6.5.2 Falling from the Sky

- Author:
- Katie Akesson

A rock is dropped from the top floor of a 500-foot tall building. A camera captures the distance the rock traveled, in feet, after each second. How far will the rock have fallen after 6 seconds? Show your reasoning.

Jada noticed that the distances fallen are all multiples of 16. She wrote down: 16 = 16 * 1 64 = 16 * 4 144 = 16 * 9 256 = 16 * 16 400 = 16 * 25 Then, she noticed that 1, 4, 9, 16, and 25 are 1², 2², 3², 4², and 5². Use Jada’s observations to predict the distance fallen after 7 seconds. Show your reasoning. (Assume the building is tall enough that an object dropped from the top of it will continue falling for at least 7 seconds.)

Write an equation for the function, with d representing the distance dropped after t seconds.