Question

The distance that an object falls from rest, when air resistance is negligible, varies directly as the square of the time that it falls (before it hits the ground). A stone dropped from rest travels 254 feet in the first 5 seconds. How far will it have fallen at the end of 8 seconds? Round your answer to the nearest integer if necessary.

Answer 1

Let the distance = d and the time = t

The distance that an object falls from rest, when air resistance is negligible, varies directly as the square of the time that it falls (before it hits the ground)

So, d = c t^2

Where c is the constant of proportion

A stone dropped from rest travels 254 feet in the first 5 seconds

So, at t = 5 , d = 254 feet

so,

254 = c * 5^2

254 = 25 c

so,

c = 254/25 = 10.16

so, d = 10.16 * t^2

To find the distance after 8 seconds, substitute with t = 8 at the final equation

So,

d = 10.16 * 8^2 = 10.16 * 64 = 650.24 feet

Rounding to the nearest integer, d = 650 feet