Answer :
Answer:
Velocity of the 24.6 g marble is 31 cm/s.
Step-by-step explanation:
Given:
Marble 1:
Mass of the marble [tex](m_1)[/tex] = 12.3 gm
Velocity of [tex]m_1[/tex] before collision [tex]v_1_i[/tex] = 15.5 cm/s
Velocity of [tex]m_1[/tex] after collision [tex]v_1_f[/tex] = 77.5 cm/s
Marble 2:
Mass of the marble [tex](m_2)[/tex] = 24.6 gm
Velocity of [tex]m_2[/tex] before collision [tex]v_2_i[/tex] = 62 cm/s
Velocity of [tex]m_2[/tex] after collision [tex]v_2_f[/tex] = ?
From the law of conservation of momentum, we know that momentum before equals the momentum after :
So,
⇒ [tex]P(i)=P(f)[/tex]
⇒ [tex](m_1\times v_1_i )+(m_2\times v_2_i) =(m_1\times v_1_f)+(m_2\times v_2_f)[/tex]
⇒ Plugging the values.
⇒ [tex](12.3\times 15.5) +(24.6\times 62)=(12.3\times 77.5)+(24.6\times v_2_f)[/tex]
⇒ [tex]190.65+1525.2=953.25+24.6\times v_2_f[/tex]
⇒ [tex]1715.85=953.25+24.6\times v_2_f[/tex]
⇒ [tex]1715.85-953.25=24.6\times v_2_f[/tex] ...subtracting both sides 953.25
⇒ [tex]762.6=24.6\times v_2_f[/tex]
⇒ [tex]\frac{762.6}{24.6}\ =v_2_f[/tex] ...dividing both sides with 24.6
⇒ [tex]31=v_2_f[/tex]
⇒ [tex]v_2_f =31[/tex] cm/s
The velocity of the 24.6 g marble after the collision is 31 cm/s and it will move opposite to of the 12.3 g marbles that is towards left.