Answer to Question #99639 in Physics for Nyx

Question

A grocery shopper tosses a(n) 8.8 kg bag of
rice into a stationary 17.8 kg grocery cart.
The bag hits the cart with a horizontal speed
of 6.6 m/s toward the front of the cart.
What is the final speed of the cart and bag?
Answer in units of m/s.
Don't round answer.

Answer 1

Let us use notation:

$m_b = 8.8 kg$, $v_b = 6.6 \frac{m}{s}$ - mass and speed of the rice bag respectively,

$m_c = 17.8 kg$ - mass of the grocery cart.

Let us use the law of conservation of momentum (total momentum before the bag hitting the cart must be equal to the total momentum when they both move together with speed $v$ after):

$m_b v_b + 0 = m_b v + m_c v$, from where $v = \frac{m_b v_b}{m_b + m_c} \approx 2.18 \frac{m}{s}$.