Final answer:
The student's question involves a perfectly inelastic collision between a snowboarder and a skier. Using the conservation of momentum and the conversion of potential to kinetic energy, we can determine their common speed after the collision.
Step-by-step explanation:
The student is asking about a scenario involving a perfectly inelastic collision between a 66 kg snowboarder and a 72 kg skier. In a perfectly inelastic collision, the two objects stick together and move with a common velocity after the collision. Since friction is negligible, we can use conservation of momentum to calculate the speed of the snowboarder and the skier after the collision.
Before the collision, the snowboarder has potential energy due to being on top of a hill 25 m high, which is converted to kinetic energy as they slide down. The potential energy is calculated as mgh, where m is mass, g is the acceleration due to gravity (9.8 m/s2), and h is the height. The kinetic energy at the bottom of the hill is the same as the potential energy at the top, which lets us determine the velocity of the snowboarder just before the collision.
The combination of his velocity due to gravity and her stationary position allows us to apply the conservation of momentum, where the total momentum before the collision (only the snowboarder's, since the skier is stationary) equals the total momentum after the collision (the combined mass moving with a common velocity). The final speed can then be calculated using the formula (m1 * v1 + m2 * v2) / (m1 + m2), where m1 and v1 are the mass and velocity of the snowboarder, and m2 and v2 are the mass and velocity of the skier.