You are trying to find out how high you have to pitch a water balloon in order for it to burst
when it hits the ground. You discover that
the balloon bursts when you have pitched it
to a height of 18 m.
With what velocity did the balloon hit
the ground? The acceleration of gravity is
9.8 m/s². The positive direction is up, so the
velocity when it hits is negative.
Answer in units of m/s.

As you are trying to move a heavy box of mass m, you realize that it is too heavy for you to lift by yourself. there is no one around to , so you attach an ideal pulley to the box and a massless rope to the ceiling, which you wrap around the pulley. you pull up on the rope to lift the box. use g for the magnitude of the acceleration due to gravity and neglect friction forces. once you have pulled hard enough to start the box moving upward, what is the magnitude f of the upward force you must apply to the rope to start raising the box with constant velocity? express the magnitude of the force in terms of m, the mass of the box.