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

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The discussion centers on calculating the time it takes for Harry to throw a boomerang to hit Tom, who is accelerating away on a motorbike. The key formula to prove is t = (1/v)[(u + v)^2/2a - d)], where 'u' is Harry's initial speed, 'v' is the maximum throw speed of the boomerang, 'a' is Tom's acceleration, and 'd' is the distance between them. Participants suggest using kinematic equations and setting the positions of Harry and the boomerang as functions of time to determine when they intersect. There is a focus on correctly substituting variables into the formula to solve the problem. Ultimately, the discussion emphasizes the need for a clear understanding of motion dynamics to find the solution.
vaishakh
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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.
 
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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.
 
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