Math Snap

STEP 1

1. The firefighter has a mass of $55.0 \, \text{kg}$.
2. The height of the stairs is $28.0 \, \text{m}$.
3. The firefighter climbs at a constant speed, implying no change in kinetic energy.
4. The work done is against gravity.

STEP 2

1. Recall the formula for work done against gravity.
2. Calculate the gravitational force acting on the firefighter.
3. Substitute the values into the work formula.
4. Calculate the work done.

STEP 3

Recall the formula for work done against gravity:
$$W = F \cdot d$$ where $F$ is the gravitational force and $d$ is the distance (height) moved in the direction of the force.

STEP 4

Calculate the gravitational force acting on the firefighter:
$$F = m \cdot g$$ where $m = 55.0 \, \text{kg}$ is the mass and $g = 9.8 \, \text{m/s}^2$ is the acceleration due to gravity.
$$F = 55.0 \, \text{kg} \times 9.8 \, \text{m/s}^2$$ $$F = 539 \, \text{N}$$

STEP 5

Substitute the values into the work formula:
$$W = F \cdot d$$ $$W = 539 \, \text{N} \times 28.0 \, \text{m}$$

Calculate the work done:
$$W = 539 \, \text{N} \times 28.0 \, \text{m}$$ $$W = 15092 \, \text{J}$$ The work done by the firefighter is:
$$\boxed{15092 \, \text{J}}$$