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 long will it take an object to fall 64 feet?
Acceleration due to gravity is 9.8 m/s2.
Our first priority is to convert this into feet to correspond to the question you present.
Acceleration due to gravity is 32 ft/s2
Henceforth, in 1 second, this object fell...
x=(1/2)(32 ft/s2)(1 s)2
x=(1/2)(32 ft/s2)(1 s2)
The unit of s2 is in the denominator and numerator. It cancels...
The only unit remaining is feet. This is what we want.
64 ft=(1/2)(32 ft/s2)(t2)
64 ft=(16 ft/s2)(t2)
Let's divide both sides by (16 ft/s2)...
(64 ft)/(16 ft/s2)=t2
The unit of feet is in the numerator and denominator. It cancels.
The unit of s2 is in the denominator of the denominator. It is now in the numerator.
Square root both sides...
It will require 2 seconds for it to fall 64 feet.