A block is projected up a rough inclined plane of angle 45^ with an initial velocity. The time taken by the block to slide back down to its starting point is twice the time it took to slide up to the highest point. The coefficient of kinetic friction between the block and the inclined plane is:

Step-by-step solution

Let the distance from the starting point to the highest point be s . For the upward motion, the acceleration (deceleration) is: a_ up = g( 45^ + _k 45^ ) For the downward motion, the acceleration is: a_ down = g( 45^ - _k 45^ ) Using the kinematic equation s = 1 2 a t^2 (which is valid for upward motion if time is measured in reverse from the highest point), we have: s = 1 2 a_ up t_ up ^2 = 1 2 a_ down t_ down ^2 Given that t_ down = 2 t_ up , we can substitute this into the equation: a_ up t_ up ^2 = a_ down (2 t