A ball with a mass of #11# #kg# moving at #18# #ms^-1# hits a still ball with a mass of #22# #kg#. If the first ball stops moving, how fast is the second ball moving? How much kinetic energy was lost as heat in the collision?

A ball that is stationary loses momentum because momentum is conserved.

Momentum prior to impact:

After rearranging, we find that the momentum following the collision will remain the same:

Before the collision, the kinetic energy is:

Following the collision, the kinetic energy is:

To find the velocity of the second ball after the collision, you can use the principle of conservation of momentum. The total momentum before the collision equals the total momentum after the collision.

Initial momentum: ( m_1 \times v_1 + m_2 \times v_2 )

Final momentum: ( m_1 \times 0 + m_2 \times v_2 )

Using the conservation of momentum equation:

( m_1 \times v_1 = m_2 \times v_2 )

( 11 , \text{kg} \times 18 , \text{m/s} = 22 , \text{kg} \times v_2 )

( v_2 = \frac{11 , \text{kg} \times 18 , \text{m/s}}{22 , \text{kg}} )

( v_2 \approx 9 , \text{m/s} )

To find the kinetic energy lost as heat in the collision, you can use the equation:

( \text{Kinetic energy lost} = \text{Initial kinetic energy} - \text{Final kinetic energy} )

( \text{Initial kinetic energy} = \frac{1}{2} \times m_1 \times v_1^2 )

( \text{Final kinetic energy} = \frac{1}{2} \times m_2 \times v_2^2 )

Substitute the given values and calculate the kinetic energy lost.