Final answer:
C) 16 ft (5 m). The maximum length of a ladder that can be carried safely by one firefighter depends on the balance between the torques caused by the weight of the ladder and the firefighter. By equating the torques and solving for the length of the ladder, we can find the maximum length. In this case, the maximum length is 16 ft (5 m).
Step-by-step explanation:
To determine the maximum length of a ladder that can be carried safely by one firefighter, we need to consider the forces acting on the ladder. The main concern is the torque or moment caused by the weight of the ladder and the distance from the center of mass to the bottom.
The maximum length of the ladder depends on the balance between the torques. To ensure stability, the counterclockwise torque due to the weight of the ladder should be equal to or smaller than the clockwise torque due to the weight of the firefighter. This means that the counterclockwise torque is calculated as:
Torque_ladder = m_ladder * g * d
where m_ladder is the mass of the ladder, g is the acceleration due to gravity, and d is the distance from the center of mass to the bottom of the ladder. The clockwise torque can be calculated similarly as:
Torque_firefighter = m_firefighter * g * (L - d)
where m_firefighter is the mass of the firefighter, and L is the length of the ladder. By equating the two torques and solving for L, we can find the maximum length of the ladder that can be carried safely by one firefighter.
In this case, we have m_ladder = 10.0 kg, m_firefighter = 70.0 kg, d = 2.0 m, and g = 9.8 m/s^2. Substituting these values, we can solve for L. Therefore, the correct option is C) 16 ft (5 m).