Ahot-air balloon is rising straight up with a speed of 4.6 m/s. a ballast bag is released from rest relative to the balloon at 13.4 m above the ground. how much time elapses before the ballast bag hits the ground?

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.

The bag makes a net displacement s of 13.4 m downwards, hence

Its initial velocity is

The acceleration due to gravity acts downwards and hence it is negative.

Use the values in the equation of motion and write an equation for t.

Solving the equation for t and taking only the positive value for t,

t=2.18 s