The number of meters, d, that a skydiver falls before her parachute opens varies directly as the square of the time, t, that she has in the air. The skydiver falls 20 meters in 2seconds how far will she fall in 2.5seconds. Round your answer to 2-decimal places and do not forget to label in lower case letters.

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• If one variable varies directly to another, they fit this equation pattern:

y = kx

Where k is some constant but results in y getting larger as x gets larger.

You are told that the number of meters a skydiver falls (d) varies directly as the square of the time (t).  So we have this equation:

d = kt²

The fall is 20 meters in 2 seconds.  We can now solve for k:

20 = k(2)²

20 = 4k

k = 5

Our equation is now:

d = 5t²

How far is the fall after 2.5 seconds?  Solve for d when t = 2.5:

d = 5(2.5)²

d = 5(6.25)

d = 31.25 meters

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• d∝ t^2.

20 ∝4,

d ∝2.5^2,

d/20 = (2.5^2)/4,

fall in 2.5 s = 31.25 m.

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