A 87.8-kg baseball player slides into second base. The coefficient of kinetic friction between the player and the ground is Hk = 0.600. (a)
What is the magnitude of the frictional force? (b) If the player comes to rest after 1.23 s, what is his initial speed?

To solve this problem, let's break it down into two parts: 

### Part (a) - Magnitude of the Frictional Force

The frictional force \( F_f \) is given by the equation:

\[
F_f = \mu_k \cdot N
\]

where:
- \( \mu_k \) is the coefficient of kinetic friction (0.600),
- \( N \) is the normal force, which is equal to the gravitational force acting on the player since he is sliding on a horizontal surface.

The gravitational force is:

\[
N = m \cdot g
\]

where:
- \( m \) is the mass of the player (87.8 kg),
- \( g \) is the acceleration due to gravity (9.81 m/s²).

Substitute the values:

\[
N = 87.8 \, \text{kg} \cdot 9.81 \, \text{m/s²} = 860.418 \, \text{N}
\]

Now, calculate the frictional force:

\[
F_f = 0.600 \cdot 860.418 \, \text{N} = 516.251 \, \text{N}
\]

Thus, the magnitude of the frictional force is approximately **516.25 N**.

---

### Part (b) - Initial Speed of the Player

To find the initial speed, we use the fact that the player comes to rest under the influence of the frictional force. The frictional force causes a deceleration \( a \), which can be found from Newton's second law:

\[
F_f = m \cdot a
\]

Rearranging for acceleration \( a \):

\[
a = \frac{F_f}{m} = \frac{516.251 \, \text{N}}{87.8 \, \text{kg}} = 5.88 \, \text{m/s²}
\]

Since the player comes to rest after 1.23 seconds, we can use the equation of motion:

\[
v_f = v_i + a \cdot t
\]

where:
- \( v_f \) is the final velocity (0 m/s, since the player comes to rest),
- \( v_i \) is the initial velocity (what we need to find),
- \( a \) is the deceleration (-5.88 m/s²),
- \( t \) is the time (1.23 s).

Rearranging to solve for \( v_i \):

\[
v_i = v_f - a \cdot t
\]

Substitute the known values:

\[
v_i = 0 - (-5.88 \, \text{m/s²}) \cdot 1.23 \, \text{s} = 7.23 \, \text{m/s}
\]

Thus, the initial speed of the player is approximately **7.23 m/s**.

---

### Summary of Answers:
(a) The magnitude of the frictional force is **516.25 N**.  
(b) The player's initial speed was **7.23 m/s**.

---

Would you like more details or have any questions about these calculations?

Here are 5 related questions to deepen your understanding:
1. How would the frictional force change if the coefficient of friction increased?
2. What happens to the initial speed if the mass of the player decreases?
3. How would the time to come to rest affect the calculated initial speed?
4. What other forces, if any, act on the player during the slide?
5. How would the problem change if the surface was inclined?

**Tip**: Always ensure the direction of forces matches the coordinate system when applying Newton’s laws.

A 87.8-kg baseball player slides into second base. The coefficient of kinetic friction between the player and the ground is Hk = 0.600. (a) What is the magnitude of the frictional force? (b) If the player comes to rest after 1.23 s, what is his initial speed?

Learn how to calculate the frictional force and initial speed of a baseball player sliding into second base. With a mass of 87.8 kg and a coefficient of kinetic friction of 0.600, this detailed solution uses Newton's second law and kinematic equations to determine the player's speed and the force involved. Suitable for high school students in Grades 11-12.

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