Answer to Question #215287 in Physics for Sera

Question

A block is started from rest at the top of an inclined plane 6 meters long which makes 45 degrees with the horizontal. The coefficient of friction between the block and the plane is 0.20. At the foot of the plane, the block continues to move along a horizontal surface. If the coefficient of friction between the block and the horizontal surface is 0.15, how far does the block go along the horizontal surface? 

Answer 1

$$mgl\sin{45}=\mu_1mgl\cos{45}+\mu_2mgd\\ l\sin{45}=\mu_1l\cos{45}+\mu_2d\\ 6\sin{45}=(0.2)6\cos{45}+0.15d\\d=23\ m$$