Question

The distance s that an object falls is directly proportional to the square of the time t of the fall. If an object falls 16 feet in 1​ second, how far will it fall in 2 ​seconds? How long will it take an object to fall 400 ​feet?

Answer 1

Answer: if S is the distance, the fact that the distance is proportional to the square of the time means that S(t) = a*
`t^(2)` where a is a constant of proportionality, with units of
`(feet)/(s^(2) )`.

We know that S(1) = 16 feet = a*1, then a = 16
`(feet)/(s^(2) )`

then S(2) = 16*4 feet = 64.

and if we want to know in how much time te objet will fall 400feet, then S(t₀) = 400 feet = 16*
`t₀^(2)`

so t₀ =
`√(400/16)` = 5s.