A 96.3-kg baseball player slides into second base. The coefficient of kinetic friction between the player and the ground is μk = 0.619. (a) What is the magnitude of the frictional force? (b) If the player comes to rest after 1.00 s, what is his initial speed?

M*g = 96.3 * 9.8=943.7 N.=Wt. of player.

= Normal force(Fn).

a. Fk = u*Fn = 0.619 * 943.7 = 584.2 N.

b. a = u*g = 0.619 * (-9.8)=-6.07 m/s^2.

V = Vo + a*t = 0.
Vo = -a*t = -(-6.07)*1.0 = 6.07 m/s.

To find the magnitude of the frictional force, we can use the formula:

frictional force = coefficient of kinetic friction * weight

Where the weight of the baseball player is given by:

weight = mass * gravitational acceleration

The formula for gravitational acceleration is:

gravitational acceleration = 9.8 m/s^2

Let's substitute the given values into the formulas:

mass = 96.3 kg
coefficient of kinetic friction (μk) = 0.619
gravitational acceleration (g) = 9.8 m/s^2

(a) To find the magnitude of the frictional force:

frictional force = μk * weight

weight = mass * gravitational acceleration
weight = 96.3 kg * 9.8 m/s^2

Now we can substitute the weight into the formula for the frictional force:

frictional force = 0.619 * (96.3 kg * 9.8 m/s^2)

Calculating the frictional force gives us:

frictional force = 0.619 * 94.35 N
frictional force ≈ 58.36 N

So, the magnitude of the frictional force is approximately 58.36 N.

(b) To find the initial speed of the baseball player, we can use the equation:

final speed = initial speed + acceleration * time

In this case, the final speed is zero (since the player comes to rest), the acceleration is the gravitational acceleration (9.8 m/s^2), and the time is given as 1.00 s.

Setting up the equation:

0 = initial speed + (9.8 m/s^2) * (1.00 s)

Simplifying the equation gives us:

initial speed = - (9.8 m/s^2) * (1.00 s)
(initial speed) * (-1) = 9.8 m/s^2 * 1.00 s
initial speed = -9.8 m/s

Therefore, the initial speed of the baseball player is -9.8 m/s. Note that the negative sign indicates that the player was initially moving in the opposite direction of the final speed.

To find the magnitude of the frictional force acting on the baseball player, we can use the formula:

Frictional force = coefficient of kinetic friction * normal force

(a) To calculate the magnitude of the frictional force, we need to determine the normal force acting on the player. The normal force is the force exerted by the ground perpendicular to the surface. In this case, since the player is sliding on the ground, the normal force is equal to the player's weight. Therefore, the normal force is:

Normal force = mass * acceleration due to gravity
= 96.3 kg * 9.8 m/s^2
= 943.74 N

Now we can calculate the magnitude of the frictional force:

Frictional force = μk * normal force
= 0.619 * 943.74 N
= 584.419 N

Therefore, the magnitude of the frictional force acting on the baseball player is 584.419 N.

(b) To find the initial speed of the player, we can use the equation:

Final velocity = Initial velocity + (acceleration * time)

Since the player comes to rest, the final velocity is zero and the acceleration can be calculated using Newton's second law:

Frictional force = mass * acceleration
584.419 N = 96.3 kg * acceleration

Solving for acceleration, we get:

acceleration = 584.419 N / 96.3 kg
= 6.06 m/s^2

Substituting this acceleration into the equation for velocity, we have:

0 = Initial velocity + (6.06 m/s^2 * 1.00 s)

Solving for the initial velocity, we get:

Initial velocity = - (6.06 m/s^2 * 1.00 s)
= -6.06 m/s

Therefore, the initial speed of the player is 6.06 m/s in the opposite direction.