What Is the Speed After Collision in a Hockey Game Physics Problem?

[Precursor]

Homework Statement

Two 72.0 kg hockey players skating at 5.45 m/s collide and stick together. If the angle between their initial directions was 115$$^{o}$$, what is their speed after the collision?

Homework Equations

p = mv
$$p_{i} = p_{f}$$

The Attempt at a Solution

$$p_{ix} = p_{fx} = 0$$

$$p_{iy} = p_{fy}$$

$$m_{A}v_{A} + m_{B}v_{B} = (m_{AB})(v_{AB})$$

$$(72)(5.45cos(32.5)) + (72)(5.45cos(32.5)) = 144v_{AB}$$

$$v_{AB} = 4.60 m/s$$

Am I correct?

 

[anathema]

I would like to offer some feedback on your solution. Firstly, it is always important to clearly define the variables you are using in your equations. In this case, it would be helpful to specify that m_A and m_B are the masses of the two players, and v_A and v_B are their initial velocities. Additionally, it would be more accurate to use the angle between their initial velocities, rather than their initial directions, in the calculation.

Furthermore, it is important to consider the conservation of momentum in both the x and y directions. While your calculation for the y component is correct, it would be more accurate to also consider the x component of momentum. This can be done by using the sine function instead of cosine, and taking into account the negative direction for one of the players.

Finally, it is always a good idea to check your units to ensure that they are consistent throughout the calculation. In this case, the mass should be in kilograms and the velocity in meters per second.

Overall, your approach is correct but there are some minor improvements that can be made to make it more accurate.