Question

The cart and package have a mass of 20 kg and 5 kg respectively. If the card has a smooth surface and it is initially at rest, while the velocity of the package is as shown, determine the final velocity of the cart and package after in the impact.

Answer 1

$m_c=20\;kg \\ m_p = 5\;kg \\ (v_p)_1=10\;m/s$

The expression of the velocity in the horizontal direction:

$(v_p)_{1H}=\frac{4}{5}(v_p)_1 \\ (v_p)_{1H}=\frac{4}{5} \times 10 = 8 \;m/s$

Since the external force is zero, therefore the momentum is conserved. Write the expression of the conservation of the momentum.

$m_c(v_c)_{1H}+m_p(v_p)_{1H}=m_c(v_2)+m_p(v_2) \\ m_c(v_c)_{1H}+m_p(v_p)_{1H}=(m_c+m_p)(v_2) \\ 20 \times 0 + 5 \times 8 = (20 + 5)(v_2) \\ v_2 = \frac{40}{25}=1.6 \;m/s$

Answer: 1.6 m/s