Understanding the Concepts

* Conservation of Energy: The total mechanical energy (potential energy + kinetic energy) of the ball remains constant throughout its motion (ignoring air resistance).

* Potential Energy: PE = mgh, where m is mass, g is acceleration due to gravity (9.8 m/s²), and h is height.

* Kinetic Energy: KE = (1/2)mv², where m is mass and v is velocity.

Steps

1. At the start: The ball has only kinetic energy (KE).

2. At the highest point: The ball momentarily stops, so its velocity is 0. At this point, all its initial kinetic energy has been converted into potential energy (PE).

Calculations

* Initial Kinetic Energy (KE):

KE = (1/2) * 0.1 kg * (29 m/s)² = 42.05 J

* Potential Energy at the Highest Point (PE):

PE = KE = 42.05 J

* Height (h):

PE = mgh

42.05 J = 0.1 kg * 9.8 m/s² * h

h = 42.05 J / (0.1 kg * 9.8 m/s²)

h ≈ 42.9 m

Answer: The ball will climb approximately 42.9 meters high.