Solving Elastic Collision Homework: Player 2's Final Velocity

In summary, a collision occurs between two football players, with player 1 having a mass of 75 kg and a velocity of 6 m/s and player 2 having a mass of 150 kg and a velocity of -3 m/s. Using the equation provided in class, the final velocity of player 2 can be calculated as 3 m/s, however, the online homework solution states that it is -3 m/s, which does not make sense. It is possible that a negative sign was missed or there is a misunderstanding of the principle of momentum.
  • #1
4
0

Homework Statement


A collision occurs between two football players. Player 1 has mass of 75 kg and a velocity of 6 m/s. Player 2 has mass of 150 kg and a velocity of -3 m/s. Assuming an ELASTIC collision, what is the final velocity of player 2?


Homework Equations


They gave us this equation in class to calculate the final velocity:
m = mass
Vi = initial velocity
Vf = final velocity
a = player 1
b = player 2

Vfb = [(2*ma)/(ma+mb)]*Via + [(mb-ma)/(ma+mb)]*Vib


The Attempt at a Solution


Using the equation above and plugging in the numbers:

Vfb =
[(2*75kg)/(75kg + 150kg)]*(6 m/s)
+
[(150kg - 75kg)/(75kg + 150kg)]*(-3 m/s)

which gives me:

Vfb = 4 m/s + -1 m/s = 3 m/s


The "online" homework solution says it is -3 m/s. Am I incorrect? Did I miss a negative sign somewhere, or is there a principle of momentum that I am not getting?
 
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  • #2
LSarah6 said:
The "online" homework solution says it is -3 m/s.
That answer implies that the velocity of the 2nd player is unchanged by the collision--which makes no sense.
 
  • #3


Your solution is correct. The final velocity of player 2 should be 3 m/s, not -3 m/s. It is possible that the online homework solution is incorrect. It is also possible that there is a mistake in the given equation or in the values provided for player 2's mass and initial velocity.

It is always important to double check your calculations and make sure you are using the correct units in your equations. If you are still unsure, you can consult with your teacher or a classmate to verify your solution. Remember, in science, it is important to always question and critically analyze the information presented to us. Keep up the good work!
 

1. What is an elastic collision?

An elastic collision is a type of collision between two objects where the total kinetic energy of the system is conserved. This means that the objects bounce off each other without any loss of energy due to deformation or heat.

2. What is the formula for calculating the final velocity of player 2 in an elastic collision?

The formula for calculating the final velocity of player 2 in an elastic collision is vf2 = [(m1-m2)*v1i + 2*m2*v2i] / (m1+m2), where vf2 is the final velocity of player 2, m1 and m2 are the masses of player 1 and player 2 respectively, and v1i and v2i are the initial velocities of player 1 and player 2 respectively.

3. How is momentum conserved in an elastic collision?

In an elastic collision, momentum is conserved because the total momentum of the system before the collision is equal to the total momentum after the collision. This means that the sum of the individual momentums of the two objects remains the same.

4. What happens in an elastic collision if the masses of the two objects are equal?

If the masses of the two objects are equal, the final velocities of both objects will be equal as well. This is because the formula for calculating the final velocity in an elastic collision is symmetrical and the masses cancel out.

5. Can the final velocity of player 2 be negative in an elastic collision?

Yes, the final velocity of player 2 can be negative in an elastic collision. This indicates that player 2 is moving in the opposite direction to its initial velocity. The negative sign does not affect the conservation of energy or momentum in the collision.

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