Final answer:
The final speed of the cart and the bag after the collision, calculated using the conservation of momentum, is approximately 1.89 m/s.
Step-by-step explanation:
The subject of the question falls under Physics, specifically it is a problem related to the conservation of linear momentum.
To find the final speed of both the grocery cart and the bag of rice after the collision, we use the principle that the total momentum before the collision is equal to the total momentum after the collision, given that no external forces are acting on the system.
The initial momentum is solely due to the bag of rice since the cart is stationary.
Therefore, the formula for initial momentum is mass of the bag times its velocity (9.3 kg × 5.8 m/s), and the final momentum is the combined mass of the cart and the bag times the final velocity ((9.3 kg + 19.3 kg) × final velocity).
Calculating this gives us:
Initial momentum = 9.3 kg × 5.8 m/s = 53.94 kg·m/s
To find the final velocity (v_f), we set the initial momentum equal to the final momentum:
53.94 kg·m/s = (9.3 kg + 19.3 kg) × v_f
v_f = 53.94 kg·m/s / (9.3 kg + 19.3 kg)
v_f = 53.94 kg·m/s / 28.6 kg
v_f = 1.8857 m/s (rounded to four decimal places)
The final speed of the cart and the bag after the collision is approximately 1.89 m/s.