A hot-air balloon and its basket are accelerating upward at 0.265 m/s2, propelled by a net upward force of 688 N. A rope of negligible mass connects the balloon and basket. The rope tension exceeds the basket's weight by 79.8 N.

Question: Find, separately, them mass of the balloon and the basket (incidentally, most of the balloon's mass is air)

The mass of the balloon is 2295 kg, and the mass of the basket is 301 kg.

Explanation:

Let us call the mass of the balloon and the mass of the basket , then according to newton's second law:

,

where is the upward acceleration, and is the net propelling force (counts the gravitational force).

Also, the tension in the rope is 79.8 N more than the basket's weight; therefore,

and this tension must equal

Combining equations (2) and (3) we get:

since , we have

Putting this into equation (1) and substituting the numerical values of and , we get:

Thus, the mass of the balloon and the basket is  2295 kg and 301 kg respectively.

t = 1/400 h   ⇔ 0.0025 h ⇔ 9s ⇔ 0.15 m

any of the answers are correct.