Question

Ball a of mass 5.0 kilograms moving at 20 meters per second collides with ball b of unknown mass moving at 10 meters per second in the same direction. after the collision, ball a moves at 10 meters per second and ball b at 15 meters per second, both still in the same direction. what is the mass of ball b? * 1 point your answer

Answer 1

10.0 kg

Step-by-step explanation:

The problem can be solved by applying the law of conservation of momentum - the total momentum before the collision must be equal to the total momentum after the collision:

`p_i = p_f\\m_A u_A + m_B u_B = m_A v_A + m_B v_B`

where:

`m_A = 5.0 kg` is the mass of ball A

`u_A = +20 m/s` is the velocity of ball A before the collision

`m_B = ?` is the mass of ball B

`u_B = +10 m/s` is the velocity of ball B before the collision (same sign of uA, since they are moving in same direction)

`v_A = +10 m/s` is the velocity of ball A after collision

`v_B = +15 m/s` is the velocity of ball B after collision

Re-arranging the equation, we can solve to find mB, the mass of ball B:

`m_B u_B - m_B v_B = m_A v_A - m_A u_A\\m_B = (m_A (v_A -u_A))/(u_B -v_B)=((5.0 kg)(10 m/s-20 m/s))/(10 m/s-15 m/s)=10.0 kg`