During the impact with the bat, how many impulses of importance are used to find the final velocity of the ball?

Question

The 200-g baseball has a horizontal velocity of 30 m/s when it is struck by the bat, B, weighing 900-g, moving at 47 m/s. During the impact with the bat, how many impulses of importance are used to find the final velocity of the ball?

Answer 1

Given your question there are 2 impulses that should be of "importance" when solving this question:

1. The impulse of the ball on the bat
2. The impulse of the bat on the ball

However, since the baseball changes momentum due to the bat, the necessary impulse to solve the question is the impulse of the bat on the baseball.

Regarding the actual solution,

First we should understand the type of question being asked.

Since we are given the velocity and mass of both the bat and ball that are colliding and we wish to find the final velocity of the ball, we are most likely dealing with a problem that deals with the conservation of momentum. We can treat this problem as a linear system.

Although not given, we will assume the system is inelastic since a ball slightly deforms to the bat when hitting at the moment of impact. Although not realistic, for simplicity I will assume the velocity of the bat is zero. In this system, momentum is conserved but kinetic energy is not.

The Conservation of Linear momentum is as follows:

Σp _initial = Σ p _final, where p is the momentum of a closed system

Thus for this problem,

(m_ball)(v_{ball initial})+(m_bat)(v_{bat initial}) = (m_ball + m_bat)(v_{ball final})+ (m_bat)(v_{bat final})

And if we substitute given values and solve for the desired final ball velocity of v_ball final, we get

V_ball final = -43.91 m/s or 43.91 m/s in the opposite direction