Question #fc71d

1 Answer
Eddie
May 9, 2017

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Using Equation of motion: #s = ut + 1/2 a t^2#, here as per the drawing, #u = 0# and #a = g#, so that: #s propto t^2 qquad triangle#

#triangle implies (2/3 h)/h = (t_1^2)/ (t_2^2) implies t_2^2 = 3/2 t_1^2 #

In addition: #t_2 - t_1 = 1#

#implies t_2^2 = 3/2 (t_2 - 1)^2 #

That is a quadratic that solves as #t_2 = 3 pm sqrt6# or #t_2 approx 0.55, 5.45 " sec"#

Clearly the first solution has no practical meaning [it is looking at possible solutions in negative time, which is just a mathematical consequence of the quadratic], so:

#t_2 = 3 + sqrt6 approx 5.45 " sec"#

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