Kinetics And Dynamics

We are given that the balloon moves downward with a constant acceleration . Let the mass of sand to be removed be , and we want the balloon to move upward with a double acceleration .

Step 1: For downward motion, the net force acting on the balloon is:

Step 2: For upward motion, the net force acting on the balloon after removing mass is:

Step 3: By equating the two forces, we can solve for , yielding the mass of sand to be removed:

Thus, the mass .