A block slide down an inclined plane of slope angle theta with constant velocity. it is the projected up the same plane with an initial velocity u. How far up the incline wil it move before coming ti rest.??

Dear Alpha

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AKASH GOYAL

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let the angle of incline is @..

it is given that block is moving with constant velocity when slides down the incline

so net force along the incline is zero or  friction force is equal to force due to gravity

 along incline..

or friction force = mgsin@ ......1

when particle moves upward both friction and gravity acts in opposite direction so

net force = mgsin@ + f(friction force)

             =mgsin@+mgsin@=2mgsin@                (from eq 1)

  net force  = m(net retardation)

               a(retardation) = -2gsin@ ..............2              (-ve sign is coz force acts in opp direction of motion)

applying , v² = u² + 2as

 finally particle stops so v becomes 0..

  so 0 = u² -2(2gsin@)s  

       s= u²/4gsin@         .......... ..3

so the block moves this much distance before coming to rest .....