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.
When a ball is thrown vertically upwards, it experiences a constant acceleration due to gravity acting in the opposite direction to its motion. The acceleration is typically denoted as "g" and has a value of approximately 9.8 m/s² near the surface of the Earth.
The relevant equation for finding the final height is:
h = (v² - u²) / (2g)
Where: h = final height v = final velocity u = initial velocity g = acceleration due to gravity
When the ball reaches its highest point, the final velocity is 0 m/s because it momentarily comes to a stop before starting to descend. Therefore, the equation becomes:
h = (0² - u²) / (2g) h = -u² / (2g)
Note that the negative sign arises because the initial velocity (u) is directed upwards, while the convention for height is typically measured upwards from a reference point. The negative sign indicates that the final height is below the initial height.
So, the formula for finding the final height of a ball thrown vertically upwards with constant acceleration is:
h = -u² / (2g)