Did I Make a Calculation Error in the Elastic Collision of Two Football Players?

[LSarah6]

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 (meaning going in an opposite direction). 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?

 

[chemisttree]

The answer is obviously wrong by inspection. For the answer to be true, the velocity of Player 2 is unchanged both in sign and magnitude... no way!

I think the equation you were given is wrong. The equations should be:

http://hyperphysics.phy-astr.gsu.edu/hbase/elacol2.html#c2

 

[Blueshift5]

I would first check my calculations and make sure I did not make any errors in plugging in the numbers or performing the calculations. I would also double check the equation given in class to ensure that it is the correct one for calculating the final velocity in an elastic collision. If my calculations are correct, I would then consider the principle of conservation of momentum, which states that in an isolated system, the total momentum before a collision is equal to the total momentum after the collision. In this case, the two players are the only objects involved in the collision and the system is isolated. Therefore, the total momentum before the collision must equal the total momentum after the collision.

Before the collision, player 1 has a momentum of (75 kg)(6 m/s) = 450 kgm/s and player 2 has a momentum of (150 kg)(-3 m/s) = -450 kgm/s. The total momentum before the collision is therefore 0 kgm/s.

After the collision, if player 2 has a final velocity of -3 m/s, it means that their momentum is (150 kg)(-3 m/s) = -450 kgm/s. This would make the total momentum after the collision also 0 kgm/s, as the conservation of momentum principle states.

Therefore, if the online homework solution states that the final velocity of player 2 is -3 m/s, it is consistent with the principle of conservation of momentum. It is possible that you may have made a mistake in your calculations or in understanding the equation given in class. I would suggest double checking your work and consulting with your teacher or a classmate to ensure that you fully understand the concept of momentum and collisions in biomechanics.