Final answer:
The tension in the rope when the gymnast climbs at a constant speed is equal to his weight, which can be calculated by multiplying the mass by the acceleration due to gravity.
Step-by-step explanation:
In order to find the tension in the rope when the gymnast is climbing at a constant speed, we can use the equation T = mg, where T is the tension, m is the mass of the gymnast, and g is the acceleration due to gravity. Since the gymnast is climbing at a constant speed, his acceleration is zero, so the tension in the rope is equal to his weight. We can calculate this by multiplying the mass of the gymnast (52.5 kg) by the acceleration due to gravity (9.8 m/s²):
T = (52.5 kg)(9.8 m/s²) = 514.5 N
Therefore, the tension in the rope when the gymnast climbs at a constant speed is 514.5 Newtons.