A1200-kg ore cart is rolling at 10.8 m/s across a flat friction-free surface. a crane suddenly drops of ore vertically into the cart. how fast does the cart move just after being loaded with the ore?

The value of the final speed depends on the mass of the ore.

Let's call m the mass of the ore. We can solve the exercise by requiring the conservation of momentum, which must be the same before and after the ore is loaded.

Initially, there is only the cart, so the momentum is

After the ore is loaded, the new mass will be (1200 kg+m), and the new speed is . The momentum p is conserved, so it is still 12960 kg m/s. Therefore, we have

and so the final speed is