An 18.0 g dart tip is shot horizontally from a toy gun. The tip collides with a 360 g polyester sphere suspended by a 0.750 m light string and gets stuck to it. The breaking strength of the string is 5.00 N. Find the tip's maximum speed, just before the collision, that will not provoke a string crack.

Calculate the speed of the second ball relative to the first during a collision pendulum experiment, where the first projectile (ball) elevates the pendulum to a maximum height of 3.0 cm and another projectile (ball) of the same mass triples the height to 9.0 cm.

A lantern with a mass of M hanging from the end of a massless chain of length L is shown below. The chain is fixed to a pivot point at the top, allowing the lantern to swing freely. A bird with a mass of m flies directly towards the lantern at a velocity $\vec{v}$ and crashes into it, becoming embedded. Determine the magnitude of minimum velocity $\vec{v}$ that the bird must have to ensure the lantern, now with the bird inside, swings completely over the top of its arc.