Question

A baseball player slides into third base with an initial speed of 4.0 m/s. If the coefficient of
kinetic friction between the player and the ground is 0.46, how far does the player slide
before coming to rest?

Answer 1

The frictional force is given by F = μmg 

where μ is the coeficient of friction. 

Work done by frictional force = Fd = μmgd 

Kinetic energy "lost" = 1/2 mv² 


Fd = μmgd = 1/2 mv² 

The m's cancel μgd = v² / 2 



d = v² / 2μg 

d = 8² / 2(0.41)(9.8) 

d = 32 / (0.41)(9.8) 

d = 7.96 

Player slides 8 m . 



Note. In your other example μ = 0.46 and v = 4 m/s 



d = v² / 2μg 




= 4² / 2(0.46)(9.8) 

= 8 / (0.46)(9.8) 

= 1.77 or 1.8 m.

Hope i Helped :D

Answer 2

The frictional force is given by F = μmg

where μ is the coeficient of friction.

Work done by frictional force = Fd = μmgd

Kinetic energy "lost" = 1/2 mv² 

Since we know that W = ΔK,

so,  Fd = μmgd = 1/2 mv²

The m's cancel μgd = v² / 2

d = v² / 2μg

d =  4² / 2(0.46)(9.81)

d =  16 / 2(0.46)(9.81)

d =  1.77

Player slides 1.77 m .