Question

Two balls have masses 32 kg and 70 kg. The 32 kg ball has an initial velocity of 96 m/s (to the right) along a line joining the two balls and the 70 kg ball has an initial velocity of −47 m/s. The two balls make a head-on elastic collision with each other. 32 kg 96 m/s 70 kg −47 m/s What is the final velocity of the 32 kg ball? Answer in units of m/s. 014 (part 2 of 2) 10.0 points What is the final velocity of the 70 kg ball? Answer in units of m/s.

Answer 1

-100.27 m/s

42.72 m/s

Step-by-step explanation:

`m_1` = Mass of first ball = 32 kg

`m_2` = Mass of second ball = 70 kg

`u_1` = Initial Velocity of first ball = 96 m/s

`u_2` = Initial Velocity of second ball = -47 m/s

`v_1` = Final Velocity of first ball

`v_2` = Final Velocity of second ball

For elastic collision

`m_(1)u_(1)+m_(2)u_(2)=m_(1)v_(1)+m_(2)v_(2)`

`v_(1)=(m_1-m_2)/(m_1+m_2)u_(1)+(2m_2)/(m_1+m_2)u_2\\\Rightarrow v_1=(32-70)/(32+70)* 96+(2* 70)/(32+70)* -47\\\Rightarrow v_1=-100.27\ m/s`

Final velocity of the 32 kg ball is -100.27 m/s

`v_2=(2m_1)/(m_1+m_2)u_(1)+(m_2-m_1)/(m_1+m_2)u_2\\\Rightarrow v_2=(2* 32)/(32+70)* 96+(70-32)/(32+70)* -47\\\Rightarrow v_2=42.72\ m/s`

Final velocity of the 70 kg ball is 42.72 m/s