Answer:
(C) 700 N
Explanation:
The given parameters are;
The mass of the mountain climber, m = 100 kg
The angle formed by the rope with the horizontal, θ = 45°
The gravitational field strength, g = 10 N/kg
The weight of the man, W = m × g
∴ W = 100 kg × 10 N/kg = 1,000 N
At equilibrium, we have;
The downward force, the weight of the man, W = The upward force, the vertical component of the tension on the two halves of the rope
We have;
W = T × sin(θ) + T × sin(θ)
∴ 1,000 N = 2 × T × sin(45°)
Therefore, we have;
T = 1,000 N/(2 × sin(45°)) = 707.106781 Newtons
Therefore, the tension in the rope is closest to (approximately) 700 N.