Explanation:
Given that,
Mass of the shopping cart, [tex]m_s=21\ kg[/tex]
Initial speed of the shopping cart, [tex]u_s=4\ m/s[/tex]
Mass of the box, [tex]m_b=7\ kg[/tex]
Initial speed of the box, [tex]u_b=0[/tex] (at rest)
They stick together and continue moving at a new velocity. It is a case of inelastic collision.
(a) The momentum of the shopping cart before the collision is given by :
[tex]p_s=m_s\times u_s\\\\p_s=21\times 4\\\\p_s=84\ kg-m/s[/tex]
(b) The momentum of the box before the collision is given by :
[tex]p_b=m_b\times u_b\\\\p_b=7\times 0\\\\p_b=0[/tex]
(c) The velocity of the combined shopping cart/box wreckage after the collision is given by using the conservation of momentum as :
[tex]m_su_s+m_bu_b=(m_s+m_b)V\\\\V=\dfrac{m_su_s+m_bu_b}{(m_s+m_b)}\\\\V=\dfrac{21\times 4+0}{(21+7)}\\\\V=3\ m/s[/tex]
Hence, this is the required solution.
