A ball, intially at the top of the inclined hill, is allowed to roll down. At the bottom its speed is 4 m/s. Next the ball is again rolled down the hill, but this time it does not start from rest. It has an initial speed of 3 m/s. How fast is it going when it gets to the bottom ?

A trolley of mass 200 kg moves with a uniform speed of 36 km/h on a frictionless track. A child of mass 20 kg runs on the trolley from one end the other (10 m away) with a speed to 4m/s relative to the trolley in a direction opposite to the trolly's motion and jump out of the trolly. What is the final speed of the trolly? How much has the trolly moved from the time the child begins to run?

When a body of mass m slides down from the top of an inclined plane and reaches the bottom its velocity becomes v. When a circular disc of the same mass is rolled down the inclined plane it acquires a velocity v_(1) . Show that , v_(1) = sqrt((2)/(3))v .

A solid cylinder rolls up an inclined plane of angle of inclination 30^(@) . At the bottom of the inclined plane the centre of mass of the cylinder has a speed of 5 "m.s"^(-1) . The distance up to which the cylinder goes up the plane is

A uniform solid spherical ball is rolling down a smooth inclined plane from a height h. The velocity attained by the ball when it reaches the bottom of the inclined plane is v. If the ball is now thrown vertically upwards with the same velocity v, the maximum height to which the ball will rise is