If you are running at a constant speed how should throw the ball in order to catch it when comes down?

To catch a ball that you have thrown while running at a constant speed, you should throw it in the opposite direction of your motion (i.e., backward) with a speed that is equal to the speed at which you are running.

Here's the idea behind this technique:

1. When you throw the ball backward with a speed equal to your running speed, it initially moves backward relative to you.

2. As the ball moves backward, you continue to run forward. This means that the distance between you and the ball increases.

3. As a result of gravity, the ball starts to fall downward and experience acceleration due to gravity.

4. While the ball is falling downward, you continue to run forward, further increasing the distance between you and the ball.

5. Eventually, the ball's downward motion due to gravity will overcome the distance advantage you gained by running forward, and the ball will begin to descend and move forward relative to you.

6. If you maintain your speed and direction, you will eventually reach a point where the ball is moving forward at the same speed as you are running. At this moment, you can extend your hand backward and catch the ball without having to stop or slow down.

This technique might not be easy at first, and it may take some practice to get the timing and speed right. But with repetition and practice, you should be able to consistently catch the ball while running at a constant speed.