Question 176409
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^2}}}



Let's find the value of "k"


{{{d=kt^2}}} Start with the given equation.



{{{144=k(3)^2}}} Plug in {{{d=144}}} and {{{t=3}}}



{{{144=k(9)}}} Square 3 to get 9



{{{144/9=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^2}}} (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^2}}} Start with the given equation.



{{{d=16(5)^2}}} Plug in {{{t=5}}}



{{{d=16(25)}}} Square 5 to get 25



{{{d=400}}} Multiply




So the object will fall 400 ft in 5 seconds.