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

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 take an object to fall 64 feet?

Answer 1

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.

Answer 2

d = kt^2

 

16 = k 1^2 = k

 

d = 16t^2

 

64 = 16t^2

 

t^2 = 4

 

t = 2 seconds to fall 64 feet

Answer 3

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.