a rough block slides down the entire length of a smooth inclined plane (angle theta). A similar but smooth block would take half the time to slide the entire length. Find the coefficient of kinetic frictions between the rough block and the incline in terms of the angle theta

The value is

Explanation:

Generally the net force acting on the smooth block is mathematically represented as

Here this force also represented as

So

=>  

Generally from  kinematic equation

   before the sliding the block was at rest so  u =  0 m/s

=>  

=>      

Generally the net force acting on the rough block is mathematically represented as    

Here is the frictional  force acting on the block which is mathematically represented as

So

generally this net force is mathematically represented as

=>  

=>  

Generally from  kinematic equation

   before the sliding the block was at rest so  u =  0 m/s

=>

= >

From the question we are told that

Squaring both sides  

=>

=>

=>  

=>  

god i hope this !