When a stone is is thrown horizontally with 2 ms from a building heigh...
Understanding the Motion of the Stone
When a stone is thrown horizontally from a height, its motion can be analyzed separately in the vertical and horizontal directions.
Vertical Motion
- The stone is affected by gravity, which acts downwards with an acceleration of approximately **9.81 m/s²**.
- The initial vertical velocity of the stone is **0 m/s** since it is thrown horizontally.
- The time taken to fall from a height of 5 meters can be calculated using the equation of motion:
h = 0.5 * g * t²
Rearranging gives us:
t = √(2h/g)
Substituting **h = 5 m** and **g = 9.81 m/s²**:
t = √(2 * 5 / 9.81) ≈ 1.01 seconds
Horizontal Motion
- The stone is thrown with an initial horizontal velocity of **2 m/s**.
- In the absence of air resistance, this horizontal velocity remains constant throughout its flight.
Acceleration Just Before Hitting the Ground
- Since the horizontal motion does not experience any acceleration, its horizontal acceleration is **0 m/s²**.
- The vertical acceleration, however, remains constant and is equal to **9.81 m/s²** due to gravity.
Conclusion
- Just before hitting the ground, the stone's total acceleration can be represented as a vector, which combines both horizontal and vertical components.
- Therefore, the stone's overall acceleration just before hitting the ground is **9.81 m/s² downwards** while its horizontal component is **0 m/s²**.
This analysis highlights the independence of vertical and horizontal motions under the influence of gravity.