For a birthday gift, you and some friends take a hot-air balloon ride. One frien

Question

For a birthday gift, you and some friends take a hot-air balloon ride. One friend is late, so the balloon floats a couple of feet off the ground as you wait. Before this person arrives, the combined weight of the basket and people is 1220 kg, and the balloon is neutrally buoyant. When the late arrival climbs up into the basket, the balloon begins to accelerate downward at 0.53 m/s^2.

What was the mass of the last person to climb aboard in kg?

Explanation / Answer

Let F be bouyancy force which is equal to 1220*g newtons Let m be mass of last person Now (1220+m)g - F = (1220+m)a => 1220*g + mg - 1220*g = (1220+m)*0.53 => mg = 646.6 + 0.53m => m = 646.6/(g-0.53) = 646.6/(9.81-0.53) = 69.677kg Hence mass of last person = 69.677 kg

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