To find the power developed by the boy, we first need to determine the force he applies to lift the mass. Since the mass is lifted at a constant velocity, the force applied must be equal to the weight

To find the power developed by the boy, we first need to determine the force he applies to lift the mass. Since the mass is lifted at a constant velocity, the force applied must be equal to the weight of the mass.

• Step 1: Calculate the weight of the mass. The weight ($W$) of an object is given by the formula:

  $$W = m \times g$$

  where $m$ is the mass and $g$ is the acceleration due to gravity. Given: Mass ($m$) = $29 \text{ kg}$ Acceleration due to gravity ($g$) = $10 \text{ m/s}^2$

  $$W = 29 \text{ kg} \times 10 \text{ m/s}^2$$ $$W = 290 \text{ N}$$

  Since the mass is lifted at a constant velocity using a single pulley system, the force ($F$) the boy applies is equal to the weight of the mass.

  $$F = 290 \text{ N}$$

• Step 2: Calculate the power developed. Power ($P$) is defined as the product of force and velocity when the force is applied in the direction of motion:

  $$P = F \times v$$

  Given: Force ($F$) = $290 \text{ N}$ Velocity ($v$) = $5 \text{ m/s}$

  $$P = 290 \text{ N} \times 5 \text{ m/s}$$ $$P = 1450 \text{ W}$$

Comparing this result with the given options:
A. 40 W
B. 100 W
C. 250 W
D. 1450 W

The calculated power matches option D.

The final answer is $\boxed{\text{D. 1450 W}}$.