Question 1139737: The distance an object falls varies directly to the square of the time it falls. A ball falls 144 feet in 3 seconds.
(a) Write the equation that relates the distance in feet, d, to the time in seconds, t.
(b) How far (in feet) will the ball fall in 6 seconds?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! direct variation equation is y = kx.
when y = d and x = t^2, the formula becomes d = k * t^2.
when d = 144 and t = 3, formula becomes 144 = k * 3^2.
solve for k to get k = 144 / 3^2 = 144 / 9.
k is the constant of variation and remains the same for all problems involved with the same equation.
when t = 6, the formula d = k * t^2 becomes d = 144/9 * 6^2 which becomes d = 144/9 * 36 which results in d = 4 * 155 = 576.
the distance in 6 seconds will be 576 feet.
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