# Football Players: Solve Sliding Distance After Collision

• Nightrider55
In summary: DIn summary, Fred (mass 60.0kg) and Brutus (mass 120kg) collide while running with a football at 6.0m/s and 4.0m/s respectively. The coefficient of kinetic friction between their uniforms and Astroturf is 0.3. Using the conservation of momentum equation, the velocity after the collision is calculated to be -2/3 m/s. The acceleration is then determined to be -2.94 m/s^2 using the equation Ax=-mew x g. The time for the slide is found to be 0.22 seconds and the distance travelled is 7.55 cm. However, the computer system may have an error as it
Nightrider55

## Homework Statement

Fred (mass 60.0kg) is running with the football at a speed of 6.0m/s when he is met head-on by Brutus (mass 120kg), who is moving at 4.0m/s. Brutus grabs Fred in a tight grip, and they fall to the ground. How far do they slide?
Part A
The coefficient of kinetic friction between football uniforms and Astroturf is 0.3.

## Homework Equations

MfVf + MbVb=(Mf+Mb)Vs
Kinematics

Ax=-mew x g

## The Attempt at a Solution

I did the problem and doubled check my work and even had a friend check it and we couldn't find a mistake but I still get it wrong

To find the velocity after the collision I used the conservation of momentum equation above and calculated the "after impact) velocity to be -2/3 m/s. I then proceeded to find the acceleration and used Ax=-mew x g and got -2.94 m/s^2. From there I solved for time by plugging the velocity and acceleration into Vfx=Vix+Ax(delta T). I got the time for
the slide to be .22 seconds. I then plugged everything into the distance kinematics equation Xf=...and I got .075 m which I then converted to 7.55 cm, but it still says its wrong. Do you see any mistakes I made?

Nightrider55 said:
To find the velocity after the collision I used the conservation of momentum equation above and calculated the "after impact) velocity to be -2/3 m/s. I then proceeded to find the acceleration and used Ax=-mew x g and got -2.94 m/s^2. From there I solved for time by plugging the velocity and acceleration into Vfx=Vix+Ax(delta T). I got the time for
the slide to be .22 seconds. I then plugged everything into the distance kinematics equation Xf=...and I got .075 m which I then converted to 7.55 cm, but it still says its wrong. Do you see any mistakes I made?

Is "it" that says the answer wrong a computer problem-system? If so, what units does it ask for the answer in? (Possibly #1 reason why the result of a correct method is rejected...) BTW, I agree with your solution (I used the "velocity-squared" equation,
(v_f)^2 = (v_i)^2 + 2a(delta_x), and found the same distance).

It wants it in cm. I don't get why it says I am wrong.

Not being there myself to see what the computer is doing, I can only be mystified. If you're sure you've used the right quantities for the problem, your method should give the correct answer.

It is conceivable that the computer system has a difficulty for this problem. The formula encoded for its calculation could be in error, or the tolerance for input answers might have been set to zero. (This happened once a ways back in a physics course here for one problem: good luck getting the computer's answer to sixteen decimal places...)

I would bring this up with the instructor and see if there is something set up wrong for that problem. It's not like that's never happened before. (Besides, I'm feeling cocky: I helped a student last week to get the instructor in a 5000-level stats course to re-examine their solution to an exam problem and find the error in the problem statement... ;-) )

Last edited:
I talked to my teacher about it and he came to the same answer when he did it. I did show answer on the website and they calculated 8.8 cm. I don't know how they got that He sent an e-mail to the website tech support to notify them of the error.

Thanks for the help!

Last edited:
I'm glad to hear the teacher agreed with us also! :) These difficulties do crop up from time to time with the computer-based systems; they aren't going to replace living instructors anytime soon...

## 1. How is sliding distance after collision calculated for football players?

The sliding distance after collision for football players is calculated by using the formula d = (m1 * v1 + m2 * v2) / (m1 + m2) * μ * g * t, where m1 and m2 are the masses of the two players, v1 and v2 are their initial velocities, μ is the coefficient of friction between the players and the surface, g is the acceleration due to gravity, and t is the time of collision.

## 2. How does the coefficient of friction affect sliding distance after collision for football players?

The coefficient of friction plays a crucial role in determining the sliding distance after collision for football players. A higher coefficient of friction means there is more resistance between the players and the surface, resulting in a shorter sliding distance. On the other hand, a lower coefficient of friction means there is less resistance, resulting in a longer sliding distance.

## 3. What factors can affect the calculation of sliding distance after collision for football players?

There are several factors that can affect the calculation of sliding distance after collision for football players. These include the mass and initial velocities of the players, the coefficient of friction between the players and the surface, the acceleration due to gravity, and the time of collision. Other factors such as the surface type and any external forces can also impact the calculation.

## 4. Is the calculation of sliding distance after collision for football players accurate?

The calculation of sliding distance after collision for football players is based on the laws of physics and can provide a general estimate of the distance. However, it may not always be 100% accurate as there are many variables and factors that can affect the outcome. Factors such as human error in measuring the initial velocities, variations in surface conditions, and unpredictable movements of the players can all contribute to a margin of error in the calculation.

## 5. How can the calculation of sliding distance after collision for football players be used in real-life situations?

The calculation of sliding distance after collision for football players can be used in real-life situations to assess the potential risk of injury for players. By understanding the factors that contribute to the sliding distance, coaches and trainers can implement strategies to minimize the risk of injury, such as improving the playing surface or training players to control their movements during collisions. It can also be used in the development of safety equipment and gear for players.

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