A ball is thrown straight upward and rises to a maximum height of 16 m above its launch point. At what height above the launch point has the speed of the ball decreased to one-half of its initial value?

At the half-velocity point, the kinetic energy is 1/4 of the maximum value (because it is propotional to V^2). The other 3/4 of the initial energy must be potential energy. Therefore it has risen to 3/4 of its maximum height (12 meters). At maximum height, all energy is potential and kinetic energy is zero.

The answer would be different if the ball had not been thrown vertically.

To solve this problem, we need to apply the laws of motion and use the concept of projectile motion. Let's break it down step by step:

1. Determine the initial velocity (v₀) of the ball when it was thrown upward. Unfortunately, this information is not provided in the question, so we cannot proceed further without that. The initial velocity is required to calculate the time of flight and other parameters.

Please provide the initial velocity of the ball, and we can continue solving the problem.