The formula for finding the final height (h) of a ball thrown vertically upwards with constant acceleration can be derived using the equations of motion.
Let's assume:
- Initial velocity (u) is the velocity at the start of the motion.
- Final velocity (v) is the velocity when the ball reaches its highest point (which is zero since it's thrown upwards).
- Acceleration (a) is the acceleration due to gravity, which is typically taken as -9.8 m/s^2 (negative because it acts in the opposite direction to the motion).
The formula for finding the final height is:
h = (v^2 - u^2) / (2a)
Since the ball reaches its highest point, the final velocity (v) is zero. Therefore, the formula simplifies to:
h = -u^2 / (2a)
Using this formula, you can calculate the final height of a ball thrown vertically upwards given the initial velocity (u) and the acceleration due to gravity (a).