A large heavy box is sliding without friction down a smooth inclined plane of inclination theta. from a point P on the bottom of the box particle is projected inside the box, with speed u(relative to box) at angle alpha with the bottom of the box.

(a)Find the distance aling the bottom of the box between the point of projection P and the point Q where the particle lands. The particle does not hit any other surface of the box

(b)If horizontal displacement of the particle w.r.t ground is zero.Find the speed of the box w.r.t the ground at the moment when particle was projected.

Three identical balls are placed on a frictionless horizontal surface touching each other. They stick to each other because of adhesive. Another ball of same radius and mass m is placed over the void created by the three balls. Find the forces applied by the balls kept on the floor to each other if the system remains in equilibrium.

A car loaded with water having total mass 1000 kg moves on a straight horizontal Road starting from rest under the action of a force of 100 Newton. The water spills throw a small hole in the bottom at a rate of 0.1 KG per second the velocity of cart after 300 seconds is nearly.

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