If we are running on a threadmill with a speed such that I appear stationary and throw a ball, will the ball go further as compared to one who throws the ball while he is standing stationary.
The concern is that though I appear stationary while I am running on a threadmill, I do have a certain speed. Therefore the ball would have some initial horizontal speed.
In laboratory (earth-fixed) coordinates, you are stationary. The motion of the treadmill will not help the ball go farther.
It you throw while failing to run on a movind treadmill (before falling off), you will be moving backwards in lab coordinates, and the ball will go less far.
Yes, if you throw a ball while running on a treadmill, the ball will travel further compared to someone who throws the ball while standing stationary. This is due to the initial horizontal speed that you have while running on the treadmill.
To understand why, let's break it down step by step:
1. When you are running on a treadmill, you are moving forward with a certain speed. Let's call this speed "v" (for simplicity).
2. When you throw the ball, it inherits your initial horizontal speed "v". So, the ball also has an initial horizontal speed equal to "v".
3. As the ball is now moving forward with the same speed as you, it has a head start in the horizontal direction compared to when you throw the ball while standing still. This means the ball covers more horizontal distance before falling to the ground.
4. In addition to the initial horizontal speed, the ball experiences the force of gravity pulling it down vertically. This force affects both the ball and you equally since you are in the same gravitational field.
5. As a result, the ball follows a curved trajectory called a parabola. The combination of the horizontal speed and the downward pull of gravity determines the ball's range (how far it travels horizontally) and vertical height.
Therefore, due to the initial horizontal speed gained from running, the ball will travel further when thrown on a treadmill compared to when thrown while standing stationary.