Answer: [tex]6016\ N[/tex]
Explanation:
Given
Mass of basket is [tex]M=260\ kg[/tex]
Mass of each person in the basket [tex]m=70\ kg[/tex]
Acceleration of balloon is [tex]a=3\ m/s^2[/tex]
Tension of the cable causes the bucket and 3 men to move upward with [tex]a=3\ m/s^2[/tex]
So, we can write
[tex]\Rightarrow T-[260+3\times 70]g=[260+3\times 70]a\\\Rightarrow T=[260+3\times 70](a+g)\\\Rightarrow T=[260+210](3+9.8)\\\Rightarrow T=470\times 12.8\\\Rightarrow T=6016\ N[/tex]
