Question

Question #fc71d

Answer 1

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"`