A block is projected upwards along a rough inclined plane with an initial velocity of 10 m s ⁻¹ . The angle of inclination of the plane is 30^ and the coefficient of kinetic friction between the block and the plane is 1 3 . The distance travelled by the block along the incline before coming to a momentary rest is (Take g = 10 m s ⁻² )

Step-by-step solution

When the block moves up the incline, both the component of gravity along the incline and the kinetic friction act downwards along the incline, opposing the motion. The magnitude of retardation of the block is given by: a = g + _k g Substituting the given values: a = 10 30^ + 1 3 (10) 30^ a = 10 ( 1 2 ) + 10 3 ( 3 2 ) a = 5 + 5 = 10 m s ⁻² Using the third equation of motion, v^2 = u^2 - 2as : 0 = (10)^2 - 2(10)s 20s = 100 s = 5 m Answer: 5 m