Question

A ball is dropped from pole ABC where B is its midpoint so AB=BC.find the ratio of time of descent from AB to BC.

Answer 1

we apply the equation :  s = u t + 1/2 a t²  ,  here  u = 0 and  a = g

         AB = 1/2 g t1²    =>  t1 = √(2 AB/ g)
           and  v = g t1  = √(2 g AB)

  For descent from AC :
         AC = 2 AB = 1/2 g t2²    =>  t2 = 2 √(AB /g)  

  Time of descent from B to C    =  t2 - t1 = (2 - √2) √(AB/g)

  Ratio of time durations =  t1 : t2-t1 
       = √2 :  (2 - √2)
       = 1 : (√2 -1)