92.0kg baseball player slides into second base. The coefficient of friction is 0.61.The player comes to rest after 1.2s find initial speed.?

Let’s use the following equation to determine the initial speed.

vf = vi + a * t

vf = 0

a = -0.61 * 9.8 = -5.978 m/s^2

0 = vi + -5.978 * 1.2

vi = 7.1736 m/s

Rounded to two significant digits, this is 7.2 m/s. I hope this is helpful for you.

We can probably safely assume that the ball field is horizontal. This lets us know that the maximum friction force is found using

F = μN

F = μmg

An impulse will result in a change in momentum

FΔt = mΔv

μmgΔt = mΔv

we know the final speed and the initial time are both zero, so we can just use the initial velocity v and total time t

μmgt = mv

v = μgt

v = 0.61(9.8)1.2

v = 7.1736

v = 7.2 m/s

when rounded to the two significant digits of the question numerals.

Note the mass of the player is not relevant.

I hope this helps.

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Another means to solve would be to use the Newtonian equation

F = ma

and realizing the friction force is causing the acceleration

μmg = ma

a = μg

then applying the Newtonian equation

v = at

v = μgt

which is identical to the first example given.