Vertical vs. Horizontal Motion in Free Fall: The Role of Air Resistance
To explore the motion of two rocks, Rock 1 and Rock 2, let's start with the initial conditions and the forces acting on them. Rock 1 is dropped from rest, while Rock 2 is thrown horizontally at a velocity of 5 m/s. These two scenarios illustrate the interplay between vertical and horizontal motion in the context of free fall.
Horizontal Motion of Rock 2
Rock 2 is thrown horizontally at a velocity of 5 m/s. Because of the lack of any horizontal forces acting on it once it has left the thrower's hand (neglecting air resistance), the horizontal velocity of Rock 2 remains constant at 5 m/s. This constancy implies that there is no horizontal acceleration acting on Rock 2. According to Newton's first law, an object in motion will stay in motion with a constant velocity unless acted upon by an external force. Therefore, the horizontal acceleration of Rock 2 is zero.
Air Resistance and Its Impact
In an atmosphere-friction free environment, both rocks will hit the ground at the same time. However, in a real-world scenario with air resistance, the situation changes.
Air resistance affects the vertical motion of Rock 2. Because Rock 2 has a horizontal component of velocity, it has to travel horizontally before it starts its descent. This additional horizontal distance means that Rock 2 has a longer total path in the vertical direction. The air resistance slows down the vertical velocity component, causing Rock 2 to take longer to reach the ground.
Magnitude of Acceleration and Gravity
Both rocks experience acceleration due to gravity. Rock 1, which is dropped, starts its descent immediately from the moment it is released. Rock 2, once thrown, is also subject to gravity once it leaves the hand. The acceleration due to gravity is constant and is approximately 9.8 m/s2, regardless of the horizontal velocity. Vertical velocity in both cases is the same, meaning Rock 1 and Rock 2 will hit the ground at the same speed.
Flat Ground and Earth's Curvature
Assuming a flat ground, the difference in hitting points is primarily due to the horizontal distance. Rock 2 hits the ground farther away due to its initial horizontal velocity, while Rock 1 hits closer to the building. However, considering the curvature of the Earth, Rock 2 has to travel a slightly longer distance. Air resistance is a significant factor in slowing down the vertical descent of Rock 2, making it take longer to reach the ground.
Conclusion
The horizontal acceleration of Rock 2 during its flight is zero because no horizontal forces act on it once it is thrown. In the real world, with air resistance, Rock 2 takes longer to hit the ground due to the horizontal component of its velocity and the additional air resistance it encounters. Both rocks hit the ground at the same vertical velocity, which is determined by gravitational acceleration.
Understanding these concepts is crucial for solving problems involving motion in physics, particularly in the analysis of free fall and the impact of air resistance.