What is the downward speed of a basketball at a vertical position of 2.50 m?

To determine the downward speed of a basketball at a height of 2.50 m, we can apply the concept of energy conservation, specifically the conservation of mechanical energy. When the basketball is dropped from a higher position, it has gravitational potential energy that converts into kinetic energy as it falls.

The potential energy (PE) at a height ( h ) is given by the equation:

[ PE = mgh ]

where ( m ) is mass, ( g ) is the acceleration due to gravity (approximately ( 9.81 , \text{m/s}^2 )), and ( h ) is the height (2.50 m in this case).

The kinetic energy (KE) of an object in motion is expressed as:

[ KE = \frac{1}{2} mv^2 ]

At 2.50 m, the basketball converts some of its potential energy into kinetic energy. Assuming it started from rest and falls freely under gravity until reaching that height, we can set the potential energy equal to the kinetic energy at the point of interest:

[ mgh = \frac{1}{2} mv^2 ]

Since mass ( m ) appears in both