How far does a baseball player slide before coming to rest at third base?

AI Thread Summary
A baseball player sliding into third base at 7.90 m/s experiences a coefficient of kinetic friction of 0.41. To determine the distance slid before coming to rest, the net force and frictional force equations can be applied. The acceleration can be calculated using the relationship between friction and gravitational force. Additionally, the equations for motion can be utilized to find the distance based on initial speed and acceleration. The energy expended during the slide can also be equated to the initial kinetic energy for a complete solution.
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Homework Statement


A baseball player slides into third base with an initial speed of 7.90 m/s. If the coefficient of kinetic friction between the player and the ground is .41, how far does the player slide before coming to rest?


Homework Equations





The Attempt at a Solution



I have absolutely no idea how to solve this question.
 
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I'll start it for you:

f(net) = ma

f(friction) = ma

mu(k)*g*m = ma

mu(k)*g = a

Then you can use these two formulas and you should be able to solve it:

a = (v(final)-v(initial))/t

d = 1/2*a*t^2 + v(initial)tJust a hint: remember that g is negative.
 
The energy the player expends sliding is frictional force times distance. The initial energy of the player coming in is (1/2)*m*v^2. Equate them.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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