6-7-09

IIT JEE Guidance › Question Of the Day questions › 6-7-09

A straight uniform rigid wire lies on a smooth table; at each end of the wire sits a grasshopper. Show that if the mass M of the wire is not too great compared to the mass m of each of the grasshoppers, they can, by simultaneous jumps with the same speed and angle of take-off, exchange ends without colliding in mid-air.

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4 Answers

gordo ·2009-07-07 00:52:23

they can basically do dat, by jumping in anti parallel directions, at an angle say $ to the orientation of the rod.., say wid a component of velocity parallel to the table say 'V' ,

so we can conserve angular momentum, get the angular velocity of the rod in the opposite sense as the jumping of the insects, say A,

and equate the time taken by the insects to jum the distance Lcos$
(Lthe length of the rod) and the time taken by the rod to cover an angle 2$...

and prove dat there exists a solution for $ in the eqn.

(feeling lazy to solve :P)

cheers!!