Final answer:
The acceleration of an object down a frictionless incline is given by the equation a = g sin θ, where g is the acceleration due to gravity and θ is the angle of the incline. This acceleration does not depend on the object's mass.
Step-by-step explanation:
The student's question relates to the acceleration of an object moving down a frictionless incline. The acceleration an object experiences while moving down an incline can be calculated using the equation a = g sin θ, where a is the acceleration, g is the acceleration due to gravity (9.8 m/s²), and θ is the angle of the incline with the horizontal. This formula assumes that friction is negligible. When there is no friction, the acceleration is the same for all objects, irrespective of their mass, because it solely depends on gravity and the incline's angle.
For an object that transitions from a frictionless incline to a rough horizontal surface, we can use the kinematic equations to determine both the speed at the bottom of the incline and the acceleration on the horizontal surface. To find the height of the incline, we could use the object's speed at the bottom and work backwards using kinematics or energy conservation principles.