Answer :
Final answer:
The horizontal force that an assistant must brace at the bottom of the ladder is 35.2 kN. (Option A).
Explanation:
To calculate the horizontal force required, we can use the principle of equilibrium, where the sum of forces in the horizontal direction is zero. The force exerted by the man climbing the ladder creates a horizontal component, which must be balanced by the horizontal component of the reaction force exerted by the ground on the ladder. First, we need to calculate the horizontal component of the weight of the man and the ladder. Then, we can use the angle of friction to determine the horizontal reaction force at the bottom of the ladder.
The horizontal component of the weight of the man climbing the ladder is calculated as F_man = W_man * sin(θ), where W_man is the weight of the man and θ is the angle of friction. Similarly, the horizontal component of the weight of the ladder is F_ladder = W_ladder * sin(θ). Adding these horizontal components gives us the total horizontal force exerted on the ladder. Using the given values, we can calculate this force, which turns out to be 35.2 kN.
Therefore, the correct option is a) 35.2 kN, as this is the horizontal force that must be braced at the bottom of the ladder to maintain equilibrium while the man climbs.
