A hot-air balloon plus cargo has a mass of 1740 {\rm kg} and a volume of 12030 {\rm m^3}. The balloon is floating at a constant height of 6.25 {\rm m} above the ground.
What is the density of the hot air in the balloon?
To find the density of the hot air in the balloon, we need to divide the mass of the air by its volume.
The mass of the hot-air balloon plus cargo is given as 1740 kg. However, this includes both the mass of the air in the balloon and the mass of the cargo. To find the mass of the air, we need to subtract the mass of the cargo from the total mass.
Let's say the mass of the cargo is 'm'. Then the mass of the air in the balloon would be (1740 kg - m).
Next, we need to find the volume of the air in the balloon. The volume of the balloon is given as 12030 m^3. However, this includes both the volume of the air and the volume occupied by the cargo. To find the volume of the air, we need to subtract the volume of the cargo from the total volume.
Let's say the volume of the cargo is 'V'. Then the volume of the air in the balloon would be (12030 m^3 - V).
Now, we can calculate the density of the hot air in the balloon by dividing the mass of the air by its volume:
Density = (Mass of the air) / (Volume of the air)
= (1740 kg - m) / (12030 m^3 - V)
Please note that we need the mass and volume of the cargo to fully solve this problem.