A body is sliding down an inclined plane of inclination `theta` with a uniform velocity. If the body is projected with a velocity u along the plane upwards, show that it will ascend a distance `u^2//4g` sin `theta` along the plane.

A body is sliding down an inclined plane having coefficient of friction 0.5. If the normal reaction is twice that of the resultant downward force along the inclined plane , then find the angle between the inclined plane and the horizontal.

Find the acceleration of a body falling down a rough plane, inclined at an angle 30^@ . The force of friction is 0.2 times the normal reaction. After descending 1m along the inclined plane, what will be the change in the sum of the potential and the kinetic energies ? Mass o the body is 1g.

A body is projected vertically upwards with an initial velocity u_1 . Another is projected with initial velocity u_2 at an angle theta with the horizontal . If both of them reach the same height ,show that sin theta=(u_1)/(u_2) .

There is an inclined plane with length 13 m, heght 5 m and mu = (1)/(3) . With what initial velocity a body is to be slided up the plane so that it just comes to rest at the top of the inclined plane ?