High School Physics

# How to find the maximum height of a ball thrown up?

Let’s see how to find the maximum height of a ball thrown up. First, you will get the formula you need to use, and then see how to use the formula to find the maximum height. We have also provided the step-by-step derivation procedure of this max height formula for vertical motion.

Maximum Height of a ball thrown vertically upward Formula

The maximum height of a ball thrown vertically upward formula: Hmax= u2/2g

How to find the maximum height of a ball thrown up?

If we know the initial velocity with which the ball is thrown vertically upward (u), then by using the formula Hmax= u2/2g, we can easily find out the maximum height of the ball thrown vertically upward. Here, g is the acceleration due to gravity (9.8 m/s2).

Deriving the formula to find out the Maximum Height of a ball thrown vertically upward

Let’s see how to derive the formula for the maximum height of a ball thrown up vertically. We will use one of the motion equations and g as the acceleration.

And the maximum height (say, Hmax) reached by the ball thrown up vertically is obtained from the formula:
v2=u2-2gh     ( under negative acceleration)  ……………… (1)

Here, v = final velocity, u = initial velocity, and h is the height.
And, g = acceleration due to gravity.

Final velocity v=0, (at the highest point the velocity becomes zero),
At the highest point, h = Hmax

we can rewrite equation (1) as follows:

0 = u– 2gHmax

or  Hmax= u2/2g (equation of maximum height)     ………. (2)

Example (numerical)

Therefore if a ball is thrown vertically upwards with 98 m/s velocity, the maximum height reached by it would be Hmax= u2/2g = (98 x98 )/(2 x 9.8) meter = 490 meters.