Final answer:
To determine the speed of the sled and the boulder after an elastic collision, we apply the conservation of momentum and kinetic energy equations. After substitutions and calculations, we match the calculated answer with the given choices to find the correct speeds post-collision.
Step-by-step explanation:
The student's question involves finding the speed of the sled and the boulder after an elastic collision. In an elastic collision, both momentum and kinetic energy are conserved. The total momentum before the collision equals the total momentum after the collision, and the same applies to the total kinetic energy.
To solve the problem, we use the equations for conservation of momentum (m1v1 + m2v2 = m1v1' + m2v2') and conservation of kinetic energy (1/2 m1v1^2 + 1/2 m2v2^2 = 1/2 m1v1'^2 + 1/2 m2v2'^2), where m1 and m2 are the masses of the boy with sled and boulder, respectively, v1 and v2 are their speeds before the collision, and v1' and v2' are their speeds after the collision.
Substitute the given values into these equations, assuming that since the lake is frictionless, v2 (speed of boulder before collision) is 0 m/s and v2' is the velocity of boulder after the collision:
- m1 = 42.5 kg (boy + sled)
- m2 = 1000 kg (boulder)
- v1 = 10.0 m/s (boy + sled before collision)
- v2 = 0 m/s (boulder before collision)
Solving the system of equations gives us the final velocities v1' and v2', which will be of the boy and sled, and boulder respectively after the collision. Given the choices, the correct answer we calculate will match one of the provided possible solutions.