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?

During a daredevil event, an archer is seen shooting an arrow while riding a bike. The arrow is shot with a speed of 40 m/s and horizontal acceleration of 0.96 m/s² at an angle of 25° with respect to the x-axis. The bike is initially at rest and then moves along the positive x-axis at an acceleration of 3.0 m/s². Determine the exact instant at which the arrow must be shot in order to reach a target 250 m east of the archer's starting location.

A racing pickup truck moving with a speed of 80.0 m/s is passing over a bridge situated at a height of 50.0 m above the water level. Below the bridge is a river in which a person is sitting in a steady boat. A person in the truck's cargo bed stretches out their hand off the bridge to deliver a parcel in the boat. Determine the horizontal distance from the boat where the person in the truck should release the parcel so that it falls exactly in the boat.