Understanding Projectile Motion
In projectile motion, the range and maximum height of a thrown object are interrelated. When a stone is thrown, it follows a parabolic trajectory, influenced by its initial velocity and the angle of projection.
Key Factors Affecting the Maximum Height
- Initial Velocity: The speed at which the stone is thrown determines both the distance it can cover and the height it can achieve.
- Angle of Projection: The angle plays a crucial role in determining the distribution of the initial velocity into horizontal and vertical components.
Calculating Maximum Height
Given that the maximum distance (range) is 500 m, we can derive the maximum height using the following relationships:
- The formula for range R is given by R = (u^2 * sin(2θ)) / g, where u is the initial velocity, θ is the angle of projection, and g is the acceleration due to gravity (approximately 9.81 m/s²).
- The maximum height H can be calculated using H = (u² * sin²(θ)) / (2g).
For maximum distance, the optimal angle of projection is 45 degrees, which simplifies the calculations.
Conclusion
Using the equations of motion and the principles of projectile trajectories, it can be derived that the maximum height of the stone thrown to cover a range of 500 m is approximately 63.75 m.
This is a theoretical value derived under ideal conditions, assuming no air resistance and perfect projection.