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?
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The distance s that an object falls is directly proportional to the square of the time t of the fall. This can be written as s = kt^2, where k is the constant of proportionality.
Given that an object falls 16 feet in 1 second, we can find the value of k. Substituting s = 16 and t = 1 into the equation gives 16 = k(1)^2, so k = 16.
The equation for the distance an object falls is therefore s = 16t^2.
To find out how far an object will fall in 2 seconds, substitute t = 2 into the equation to get s = 16(2)^2 = 64 feet.
To find out how long it will take an object to fall 400 feet, substitute s = 400 into the equation and solve for t. This gives 400 = 16t^2, so t^2 = 400/16 = 25, and t = sqrt(25) = 5 seconds.
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