A ball with a mass of #6 kg# moving at #4 m/s# hits a still ball with a mass of #3 kg#. If the first ball stops moving, how fast is the second ball moving?

Question

A ball with a mass of #6 kg# moving at #4 m/s# hits a still ball with a mass of #3 kg#.  If the first ball stops moving, how fast is the second ball moving?

Olivia Askew · Accepted Answer

#8# meters per second

We use the law of conservation of momentum, which states that, #m_1u_1+m_2u_2=m_1v_1+m_2v_2# where: #m_1,m_2# are the masses of the two objects #u_1,u_2# are the initial velocities of the two objects #v_1,v_2# are the final velocities of the two objects So, here we get: #6 \ "kg"*4 \ "m/s"+3 \ "kg"*0 \ "m/s"=6 \ "kg"*0 \ "m/s"+3 \ "kg"*v_2# #24 \ "kg m/s"=3 \ "kg"*v_2# #v_2=(24color(red)cancelcolor(black)"kg""m/s")/(3color(red)cancelcolor(black)"kg")# #=8 \ "m/s"#

Nicholas Agrusa · Answer

undefined To solve this problem, we can use the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.

Before the collision:
Total momentum = mass of first ball * velocity of first ball + mass of second ball * velocity of second ball

After the collision:
Total momentum = mass of first ball * velocity of first ball (since the second ball is initially still)

Setting these equal to each other:

mass of first ball * velocity of first ball = (mass of first ball + mass of second ball) * velocity of second ball

Substituting the given values:

6 kg * 4 m/s = (6 kg + 3 kg) * velocity of second ball

Solving for the velocity of the second ball:

24 kg*m/s = 9 kg * velocity of second ball

velocity of second ball = 24 kg*m/s / 9 kg = 2.67 m/s

So, the second ball is moving at a speed of 2.67 m/s after the collision.