Why is this following situation impossible? A normally proportioned adult walks briskly along a straight line in the +x direction, standing straight up and holding his right arm vertical and next to his body so that the arm does not swing. His right hand holds a ball at his side a distance h above the floor. When the ball passes a point marked as x=0 on the horizontal floor, he opens his fingers to release the ball from rest relative to his hand. The ball strikes the ground for the first time at position x=7.00h
The situation described is impossible because it violates the laws of physics, specifically the concept of freefall.
When the ball is released from the person's hand, it would accelerate downwards due to gravity. This acceleration is constant (denoted as 'g') regardless of the initial height or horizontal motion.
In this scenario, the ball would fall to the ground under gravity alone, without any external forces acting on it horizontally to cause it to move along the straight line in the +x direction. The horizontal motion of the person walking briskly does not affect the vertical motion of the ball.
According to the laws of physics, the time it takes for an object to fall from rest to the ground is determined by the height from which it is dropped and the acceleration due to gravity. The time it takes for the ball to strike the ground can be calculated using the formula:
t = √(2h / g)
where:
t = time
h = height of the ball from the ground
g = acceleration due to gravity (approximately 9.81 m/s^2)
The given situation states that the ball strikes the ground at x = 7.00h, which implies a horizontal displacement. However, the vertical motion of the ball is independent of the horizontal motion, so it would not be able to strike the ground at a specific position related to the release height. Therefore, this situation is impossible.
To understand why this situation is impossible, let's break it down step by step.
1. The adult walks briskly along a straight line in the +x direction, holding his arm vertical and next to his body without swinging it. This means that the adult maintains a consistent height h throughout the motion.
2. At the point marked as x=0 on the horizontal floor, the adult releases the ball from rest relative to his hand by opening his fingers. The ball is now free to move independently.
3. The ball strikes the ground for the first time at position x=7.00h. This means that the ball has traveled a distance of 7 times the height h.
Now, let's consider the reasons why this situation is impossible:
1. Gravity: When the ball is released from the adult's hand, it is subjected to the force of gravity. Gravity causes all objects to accelerate downward at a constant rate (approximately 9.8 m/s^2 on Earth). As a result, the ball will start to fall immediately after it is released.
2. Ball Height: Since the adult is holding the ball at a height h and it falls for a distance of 7.00h, the ball would need to cover a distance greater than 7 times its initial height h to reach the ground. This is not possible unless there is an external force acting on the ball to provide additional downward acceleration.
3. Horizontal Motion: The adult is walking in a straight line without swinging his arm. As a result, the ball will move horizontally along with the adult's motion. The ball will not experience any horizontal acceleration or remain stationary relative to the adult unless another force is acting on it.
Based on these reasons, it is clear that the described situation is impossible. The ball would fall immediately after it is released from the adult's hand, and it would not be able to travel a distance of 7.00h horizontally without external factors or forces being involved.