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.

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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.

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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.

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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.