Final answer:
The speed of the large cart after the collision is 0.1096 m/s.
Step-by-step explanation:
In this scenario, we can use the law of conservation of momentum to find the speed of the large cart after the collision. According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision.
Before the collision, the momentum of the small cart is given by:
Momentum = mass x velocity = (0.2 kg) x (1.9 m/s) = 0.38 kg·m/s
After the collision, the momentum of the small cart is:
Momentum = mass x velocity = (0.2 kg) x (-0.84 m/s) = -0.168 kg·m/s
Since the large cart is at rest initially, its momentum before the collision is zero. Therefore, the total momentum before the collision is 0.38 kg·m/s.
The total momentum after the collision is the sum of the momentum of the small cart and the momentum of the large cart:
Total Momentum after collision = momentum of small cart + momentum of large cart
Total Momentum after collision = -0.168 kg·m/s + momentum of large cart
Solving for the momentum of the large cart, we find:
Momentum of large cart = Total Momentum after collision - momentum of small cart
Momentum of large cart = 0.38 kg·m/s - (-0.168 kg·m/s) = 0.548 kg·m/s
Finally, we can use the equation for momentum to find the speed of the large cart:
Momentum = mass x velocity
0.548 kg·m/s = (5 kg) x velocity
Therefore, the speed of the large cart after the collision is 0.1096 m/s.