SOLUTION: The distance that a freely falling body falls varies directly as the square of the time it falls. If a body falls 144 feet in 3 seconds, how far will it fall in 5 seconds? thank

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Question 176409This question is from textbook college algebras
: The distance that a freely falling body falls varies directly as the square of the time it falls. If a body falls 144 feet in 3 seconds, how far will it fall in 5 seconds? thank you for your help with this.
As of right now I have 144/y=3^2/5^2 am I on the right track? This question is from textbook college algebras

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let d=distance and t=time

"The distance that a freely falling body falls varies directly as the square of the time it falls" means that d=kt%5E2


Let's find the value of "k"

d=kt%5E2 Start with the given equation.


144=k%283%29%5E2 Plug in d=144 and t=3


144=k%289%29 Square 3 to get 9


144%2F9=k Divide both sides by 9.


16=k Divide.


So the value of k is k=16

This means that the equation is d=16t%5E2 (after plugging in k=16)

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Now let's answer the main question: "If a body falls 144 feet in 3 seconds, how far will it fall in 5 seconds?"



d=16t%5E2 Start with the given equation.


d=16%285%29%5E2 Plug in t=5


d=16%2825%29 Square 5 to get 25


d=400 Multiply



So the object will fall 400 ft in 5 seconds.