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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?

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Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
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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.
Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
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d = kt^2
 
16 = k 1^2 = k
 
d = 16t^2
 
64 = 16t^2
 
t^2 = 4
 
t = 2 seconds to fall 64 feet
Jude S. | Tutoring By Jude-Elementary and Special NeedsTutoring By Jude-Elementary and Special ...
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You actually need more information, but if the objects are the same size, they will fall at the same rate, as they displace the same amount of gravity. So the answer is 64'. Remember-this is assuming they are the same size object.

Comments

Hi Jude;
Acceleration due to gravity is universally the same, 9.8 m/s2, 32 feet/s2.  Size is a non-issue.  Weight is an issue for maximum velocity only because the greater the weight the greater the ability to fight air resistance.