Final answer:
After a brother and sister with equal masses collide on sleds with one being stationary and the other moving at 10 m/s, and the sleds stick together, their final velocity will be 5 m/s in the direction the brother was initially traveling, as determined by the conservation of momentum.
Step-by-step explanation:
When a brother and sister who both have the same mass are involved in a collision while sledding, and the sleds stick together, we can find their final velocity by applying the principle of conservation of momentum. In this scenario, the brother sleds into his stationary sister at 10 m/s, and they stick together after the collision. We can assume the system is isolated and no external forces are acting on it, so the total momentum before the collision equals the total momentum after the collision.
The initial momentum of the brother is his mass times his velocity (m * 10 m/s), while the initial momentum of the sister is zero, since she is at rest. When they collide and stick together, their combined mass is twice the individual mass of one child (2m), and they move off with a new velocity (V). Therefore, the final momentum of the system is (2m * V).
Setting the initial momentum equal to the final momentum, we get: (m * 10 m/s) + (m * 0 m/s) = (2m * V). Simplifying this equation, we find V = 5 m/s. Thus, the final velocity of both children after they collide and stick together is 5 m/s in the direction the brother was initially traveling.