Ballistic Pendulum Practice Problems

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 vertical and horizontal components of the pendulum’s maximum displacement when a 29-g steel ball launched at 211 m/s embeds itself in a 3.5-kg pendulum hanging from a 2.9-m-long wire, causing the pendulum to swing upward in an arc.

Calculate the speed of the second ball relative to the first during an 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.