Answer:
V_c=5.037 m/s
Step-by-step explanation:
SOLUTION:
applying the conversation of energy, taking the datum at B


V_b=(m_c+m_b)gh_a=(3+0.5)*9.81*0=0 J
V_b=4.95 m/s
applying the conversation of linear momentum,
(m_c+m_b)V_b=m_c*V_c+m_b*V_b
V_b=6*V_c-34.66 (1)
utilising the relative velocity relation,
V_b/c=V_b-V_c
V_b=0.6-V_c (2)
from (1) (2)
6*V_c-34.66=0.6-V_c
7*V_c=35.26
the final velocity of the cart is
V_c=5.037 m/s
into (2)
V_b=0.6-V_c
V_b=0.6-5.037
= 4.437