Final answer:
The boy exerts a 11.0 N force parallel to the motion of the sled over a distance of 2 m. Therefore, the work done by the boy on the sled is calculated as W = Fd cos(theta) = (11.0 N)(2 m) = 22.0 joules.
Step-by-step explanation:
To solve the mathematical problem regarding the work done by a boy on a sled, we have to use the work-energy theorem.
The work done by a force is given by the equation W = Fd cos(θ), where F is the force applied, d is the distance over which the force is applied, and θ is the angle between the force and the direction of motion.
In this scenario, the boy exerts a force of 11.0 N at an angle above the horizontal, moving the sled which has a mass of 6.40 kg over a horizontal distance of 2 m. To solve the mathematical problem completely, we assume that only the component of the force that is in the direction of the sled's motion does work. Hence, the horizontal component of the 11.0 N force is 11.0 N * cos(0°) = 11.0 N, as the force is directly above the horizontal (parallel to the motion of the sled).
The work done by the boy is then calculated as W = (11.0 N)(2 m) = 22.0 J. So, the work done by the boy on the sled is 22.0 joules.