A sled initially at rest has a mass of 47.2 kg, including all of its contents. A block with a mass of 14.5 kg is ejected to the left at a speed of 13.5 m/s. What is the speed of the sled and the remaining contents?

To find the final speed of the sled and its remaining contents, we can use the principle of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event, assuming no external forces are acting.

The momentum of an object is given by the product of its mass and velocity. The momentum of the ejected block (to the left) can be calculated by multiplying its mass (14.5 kg) with its velocity (-13.5 m/s, since it is moving in the opposite direction). The momentum of the sled and remaining contents can be calculated by multiplying their combined mass (47.2 kg) with their velocity (which we want to find).

Using the conservation of momentum, we can set up an equation:

(mass of block * velocity of block) = (mass of sled and contents * velocity of sled and contents)

(14.5 kg * -13.5 m/s) = (47.2 kg * velocity of sled and contents)

Now we can solve for the velocity of the sled and its remaining contents:

velocity of sled and contents = (14.5 kg * -13.5 m/s) / 47.2 kg

velocity of sled and contents = -4.15 m/s

Therefore, the speed of the sled and its remaining contents is -4.15 m/s. The negative sign indicates that the sled and its contents are moving to the left, in the opposite direction of the ejected block.