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Naily [24]
3 years ago
8

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 fall in 2 ​seconds? How long will it take an object to fall 400 ​feet?
Mathematics
1 answer:
Lemur [1.5K]3 years ago
7 0

Answer: if S is the distance, the fact that the distance is proportional to the square of the time means that S(t) = a*t^{2} where a is a constant of proportionality, with units of \frac{feet}{s^{2} }.

We know that S(1) = 16 feet = a*1, then a = 16\frac{feet}{s^{2} }

then S(2) = 16*4 feet = 64.

and if we want to know in how much time te objet will fall 400feet, then S(t₀) = 400 feet = 16*t₀^{2}

so t₀ = \sqrt{400/16} = 5s.

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