A block kept on a inclined plane slides down the plane with constant velocity when the slope angle of the plane is `theta`. It is then projected up with an initial velocity u. How far up the incline will it move before coming to rest ? Will it slide down again ?

Answer

`mu^(2)//4gsintheta`, No

Explanation

From problem (6) `mu_(k)=tantheta a=-(gsintehta+tantheta gcostheta)=-2gsintheta`, `v^(2)=u^(2)+2as`, `s=u^(2)//4gsintheta`. `mu_(k) lt mu_(s)`, So `theta_(k) lt theta_(s)`. When the block is rest at the top of the plane the slope angle is less than that needed to slide down from rest. So the block will not slide down again.