Solving Harry's Boomerang Problem: Find Tom's Reaction Time

[vaishakh]

Have a look at this question. Tom who is standing on a straight road notices Harry approaching him looking rather angry. Sensing the danger Tom starts his motorbike with a constant acceleration 'a' and assume that Harry is traveling. The question is that Harry has a boomerang with e can throw at a maximum speed of v in relative to himself. Then find the time Harry with himself to throw the boomerang such that it hits Tom.
It was given to prove that t = (1/v)[(u + v)^2/2a - d)]. I tried with all kinematical equations. I substituted proper variables in the formula but couldn't reach anywhere.

 

[Galileo]

My guess would be to write the position of Harry as a function of time and the position of the boomerang as a function of time and see when they are equal.