SOLUTION: If a body travels half its total path in the last 1.70 s of its fall from rest, find the total time of its fall (in seconds).

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Question 1047597: If a body travels half its total path in the last 1.70 s of its fall from rest, find the total time of its fall (in seconds).
Answer by ikleyn(52756) About Me  (Show Source):
You can put this solution on YOUR website!
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If a body travels half its total path in the last 1.70 s of its fall from rest, find the total time of its fall (in seconds).
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Let "t" be the total time of the body falling.

Then H = %28gt%5E2%29%2F2 is the total path (total height).

The path the body fell from the beginning (from the start) to the last 1.70 s of its fall is  h = %28g%28t-1.7%29%5E2%29%2F2.

According to the condition, H = 2h, which gives you an equation

%28gt%5E2%29%2F2 = 2%2A%28g%28t-1.7%29%5E2%29%2F2.

Cancel factor "g" in both sides and simplify. You will get

t%5E2 = 2%2A%28t-1.7%29%5E2,  or

t%5E2 = 2%2At%5E2+-+2%2A2%2A1.7+%2B+2%2A1.7%5E2,   or

t%5E2+-+4%2A1.7%2At+%2B+2%2A1.7%2A2 = 0.


Solve this quadratic equation for "t" to get the answer.


I am leaving it to you.