Understanding the Problem
When a ball is thrown vertically upwards with an initial speed u, it eventually reaches its highest point before descending. The distance covered during the last t seconds of its descent can be calculated using kinematic equations.
Key Concepts
- Initial Speed (u): The speed at which the ball is thrown upwards.
- Acceleration (g): The acceleration due to gravity, approximately 9.81 m/s² (acting downwards).
- Time of Descent: The total time taken for the ball to return to the original position after being thrown.
Distance Covered in Last t Seconds
To find the distance covered during the last t seconds of descent, we can utilize the following concepts:
- Total Time of Flight (T): The total time until the ball returns to the ground is given by T = (2u/g).
- Distance Formula: The distance covered in a specific time interval can be found using the formula:
*Distance = u*t + (1/2)*(-g)*t²*
- Distance in Last t Seconds: The distance covered in the last t seconds of descent can be computed as:
- Distance = Distance covered in T seconds - Distance covered in (T-t) seconds.
This will yield the distance traveled specifically during the last t seconds of its descent.
Final Formula
The final formula for the distance covered during the last t seconds of descent can be simplified as follows:
- Distance = u*t - (1/2)*g*t²
This equation effectively captures the motion of the ball during its downward trajectory, considering both its initial velocity and the effect of gravity.
Conclusion
Understanding these principles and equations is crucial for solving problems related to projectile motion in physics, specifically in scenarios like NEET.