Question

(1-Dimensional Collision) A 100g solid ball approaches a 1kg solid ball which is initially at rest. If the initial speed of the 100g ball is 5m/s, what are the final speeds of the balls?

Answer 1

Let a 100g solid ball have $m_A$ and velocity $v_B$

Let a 1000g solid ball have $m_B$ and velocity $v_A$

$m_Au_A+m_Bu_B=m_Av_A+m_Bv_B$

$0.5+0=0.1v_A+v_B$

$0.5_Au_A+0=0.1v_A+v_B$

$5=v_A+10v_B..........(1)$

If the collision is elastic (e=1)

$v_B-v_A=v_A-v_B$

$v_B-v_A=u_A$

$v_B-v_A=-5.........(2)$

Compairing the 2 equations

$v_A=v_B-5$

$5=-5 +v_B+10v_B$

$10=11v_B$

$v_B=0.909 m/s$

$v_A=0.909-5=-4.091 m/s$