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# if an object falls 16 feet in 1 second, how far will it take an object to fall 64 feet?

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 take an object to fall 64 feet?

Hi Crys;
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?

s=(1/2)gt2
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...
x=(1/2)(32 ft)
The only unit remaining is feet.  This is what we want.
x=16 feet

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.
(64/16)(s2)=t2
4 s2=t2
Square root both sides...
2 s=t
It will require 2 seconds for it to fall 64 feet.