a police inspector in a jeep is chasing a pickpocket on a straight road. the jeep is going with maximum speed v(assumed uniform). the pick pocket rides on the motor cycle of a waiting friend when the jeep is at a distance of 'd' away, the motorcycle starts with a constant acceleration a. show that the pick pocket will be caught if "v" is equal to or greater than "root over 2ad"

Asked by riya sinha | 25th Jun, 2013, 04:52: PM

Expert Answer:

You might have studied quadratic equations, right? For a given quadratic equation, if you have to determine the roots are real, then you use that Discriminant (D) >=0
Here also, in this case, since we have a quadratic equation in t 
at^2 -2vt+2d = 0
And now, for the pick pocket to be caught, this equation should result in a real value of t. Hence, D for that matter needs to be greater than or equal to 0. 
Now, for a given quadratic equation, ax^2 + bx+c = 0, 
D  = b^2 - 4ac
So, in the above quadratic equation, b = -2v and a = a and c = 2d
Hence D = (-2v)^2 - 4*a*2d >=0
4v^2 -8ad >=0
Hence proved. 

Answered by  | 26th Jun, 2013, 04:27: AM

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