There is an inclined plane on a table which is 45^o angle to the horizontal plane of the table.

i) If the potential energy of a system is P =mgh and the kinetic energy of the system is =1/2mv^2. If the system is frictionless, derive an equation for the final velocity of the cart when it reaches to the position B.

ii) If mass of the cart is 150 g and height to the point A from the plane of the table is 10 cm calculate the final velocity of the cart to the direction of the movement when it reach to the position B.

iii) The cart take 20 s to come from point A to point B, calculate the average acceleration.

iv) What is the momentum gain by the cart at position B to the direction of movement?

v) Calculate the momentum of the cart at point B to the horizontal direction.

vi) If the acceleration of the cart is constant throughout its motion, calculate the distance from A to B.