A 5-kg tool bag is attached to a pulley system in order to transport it from the ground floor to the higher floors of the construction site with an upward velocity of 12 m/s. It contains a 3-kg toolbox. For some unknown reason, it opens and a 500-g spring launches itself from inside it with an initial velocity of 10 m/s perpendicular to the path of the ascending tool bag. 3 seconds later, this spring hits the ground. Assume that the tool bag continues its rise at a constant speed of 12 m/s. Upon hitting the floor, how far is the spring from the tool box?
Twenty magic balls each weighing a quarter of a kilogram are contained in a thin bag of negligible weight. This bag of magic balls is carried by a 90-kg floating genie descending with a constant downward velocity of 8 m/s. One of the magic balls is thrown from the bag initially at 6 m/s perpendicularly to the downward path of the genie. This is measured relative to a stationary speed meter in the bag. After 12 s, the genie sees the thrown magic ball bounce for the first time. Calculate how far the genie was from the ground when the magic ball was thrown. Assume that the genie continues his descent at a constant speed of 8 m/s and he can be treated like a point-like object.