Final answer:
Using Newton's second law and the acceleration data given, the mass of the last person to climb aboard the hot-air balloon is calculated to be approximately 57 kg.
Step-by-step explanation:
The student's question asks about the mass of the late person boarding a hot-air balloon that was initially neutrally buoyant but begins to accelerate downward upon their arrival. The provided information allows us to calculate the additional force caused by the late friend's weight and use this to determine their mass by utilizing Newton's second law of motion (F = ma).
Initially, the balloon is neutrally buoyant, which means the force of gravity (Fg) acting on the balloon and its contents is balanced by the buoyant force (Fb) of the air it displaces. When the friend arrives, their mass adds to the system, and the balloon starts to accelerate downward at a rate of 0.49 m/s2. This acceleration indicates that the gravitational force has increased due to the added mass. Since we know the initial mass (mi) of the system and the acceleration (a), we can find the net force (Fnet) acting on the balloon after the person climbs aboard.
Now, let's calculate the net force using Newton's second law:
- Fnet = mi × a
- Fnet = (1140 kg) × (0.49 m/s2)
- Fnet = 558.6 N
The net force is also the difference in gravitational force before and after the last person joined, which can be equated to the weight of the late person:
- Weightlate person = masslate person × g
- Weightlate person = Fnet
- masslate person = Fnet / g
- masslate person = 558.6 N / 9.8 m/s2
- masslate person = 57 kg (approximately)
The mass of the last person to climb aboard the hot-air balloon is approximately 57 kg.