The time taken by the ballast bag to reach the ground is 2.18 s
The ballast bag at rest with respect to the balloon has the upward velocity (u) of 4.6 m/s , which is the velocity of the balloon. When it is dropped from the balloon, its motion is similar to an object thrown upwards with an initial velocity u and it falls under the acceleration due to gravity g.
Taking the upward direction as positive and the downward direction as negative, the following equation of motion may be used.
[tex] s=ut+\frac{1}{2}at^2 [/tex]
The bag makes a net displacement s of 13.4 m downwards, hence
[tex] s=-13.4 m [/tex]
Its initial velocity is
[tex] u=+4.6 m/s [/tex]
The acceleration due to gravity acts downwards and hence it is negative.
[tex] g=-9.8 m/s^2 [/tex]
Use the values in the equation of motion and write an equation for t.
[tex] s=ut+\frac{1}{2} at^2
\\ -13.4=4.6t-\frac{1}{2}(9.8)t^2\\ 4.9t^2-4.6t-13.4=0 [/tex]
Solving the equation for t and taking only the positive value for t,
t=2.18 s
