A person sitting in an open car moving at constant velocity throws a ball vertically up into air. The ball fall

The correct answer is Exactly in the hand which threw it up.

To understand why this happens, we can analyze the motion of the ball using the concepts of inertia and projectile motion.

1. Horizontal Motion and Inertia:
Before the ball is thrown, it is in the hand of the person sitting inside the car. Since the car is moving at a constant horizontal velocity, both the person and the ball share this same horizontal velocity. According to Newton's first law of motion (the law of inertia), an object in motion will continue in its state of motion with the same speed and in the same direction unless acted upon by an external force. When the ball is thrown vertically upward, no horizontal force acts on it (neglecting air resistance). Therefore, the ball maintains its initial horizontal velocity, which is exactly equal to the velocity of the car.

2. Relative Positions over Time:
Let the constant horizontal velocity of the car and the initial horizontal velocity of the ball be represented by:

$v_x$

At any time $t$ during the flight of the ball, the horizontal distance traveled by the car is:

$d_{\mathrm{car}}=v_x\times t$

Similarly, since the horizontal velocity of the ball remains constant at $v_x$, the horizontal distance traveled by the ball is:

$d_{\mathrm{ball}}=v_x\times t$

Since both the car and the ball cover the same horizontal distance in the same time:

$d_{\mathrm{car}}=d_{\mathrm{ball}}$

This means that throughout the flight, the ball remains directly above the hand of the person. As the ball comes down due to the acceleration of gravity in the vertical direction, it will land exactly back in the hand that threw it.