Solving Collision Between 120kg Tackler and 75kg Halfback

[rueberry]

I have been working on this for some time, maybe I'm just using the wrong formula.

A 120 kg tackler traveling 3 m/sec tackles a 75 kg halfback running 6m/sec in the opposite direction. What is their common speed immediately after the collison?

Thank you.

 

[Gelsamel Epsilon]

Use the formula

(M1 x U1) + (M2 + U2) = (M1 x V1) + (M2 x V2), Conservation of momentum forumla.

where M1 = Tackler Mass
M2 = Halfback Mass
U1 = Tackler Speed
U2 = Halfback speed
V1 = V2 (since the speed after colision is common) = Speed of both of them after the collision.

 

[quicknote]

I would approach this problem by using the principles of Newton's laws of motion and the conservation of momentum. The formula for momentum is mass times velocity (p=mv), and according to Newton's third law, for every action, there is an equal and opposite reaction.

In this scenario, the tackler and halfback are experiencing equal and opposite forces upon collision. Therefore, the total momentum before the collision is equal to the total momentum after the collision. We can set up the equation as follows:

(120 kg)(3 m/s) + (75 kg)(-6 m/s) = (195 kg)(v)

Where "v" is the common speed after the collision.

Solving for "v," we get a common speed of -1.23 m/s. This negative sign indicates that the two players will move in the opposite direction after the collision. This makes sense as the tackler is initially moving towards the halfback, and the halfback is moving in the opposite direction.

It is also important to note that this calculation assumes an idealized scenario with no external forces acting on the players, and the collision is perfectly elastic (meaning no energy is lost during the collision). In reality, factors such as friction and the players' body structure may affect the final outcome of the collision. Therefore, the calculated result may not be entirely accurate, but it provides a good estimate of the common speed after the collision.

In conclusion, to solve this collision between the 120 kg tackler and 75 kg halfback, we can use the principles of momentum and Newton's laws of motion. By setting up and solving an equation, we can determine the common speed of the two players after the collision.