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For a body falling freely from rest​ (disregarding air​ resistance), the distance the body falls varies directly as the square of the time. If an object is dropped from the top of a tower 512512 feet high and hits the ground in 88 ​seconds, how far did it fall in the first 55 ​seconds?

Answer :

Answer:

The distance is 199.98 ft.

Explanation:

Given that,

Distance = 512 feet

Time = 88 sec

The distance the body falls varies directly as the square of the time.

[tex]s\propto t^2[/tex]

[tex]s=kt^2[/tex]

We need to calculate the value of constant

Put the value into the formula

[tex]512=k\times(88)^2[/tex]

[tex]k=\dfrac{512}{(88)^2}[/tex]

[tex]k=0.06611[/tex]

We need to calculate the distance

Using formula of distance again

[tex]s=kt^2[/tex]

Put the value into the formula

[tex]s=0.06611\times(55)^2[/tex]

[tex]s=199.98\ ft[/tex]

Hence, The distance is 199.98 ft.

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