Final answer:
The buoyant force on the hot-air balloon and person system is 885.5 N.
Step-by-step explanation:
To calculate the buoyant force on the hot-air balloon and person system, we first need to determine the total weight of the system. The weight is equal to the mass of the system multiplied by the acceleration due to gravity.
The total mass of the system is the sum of the mass of the hot-air balloon and the mass of the person:
60 kg + 50 kg = 110 kg.
The weight of the system is given by:
weight = mass * acceleration due to gravity
= 110 kg * 9.8 m/s²
= 1078 N.
Since the system is accelerating upwards, we need to subtract the net force exerted by the system to get the buoyant force. The net force can be calculated as:
net force = mass * acceleration = 110 kg * 1.75 m/s² = 192.5 N.
The buoyant force is then given by:
buoyant force = weight - net force
= 1078 N - 192.5 N
= 885.5 N.
Therefore, the buoyant force on the system is 885.5 N.