A body is thrown vertically upwards with an initial velocity u. Write an expression for the maximum height attained by the body.

As we know,

v² = u² - 2gh

Initial velocity = u

Final velocity = 0

Substituting the values in the formula above we get,

$0^2 = u^2 - 2gh${max} \\[0.5em] 2gh{max} = u^2 \\[0.5em] \Rightarrow h_{max} = \dfrac{u^2}{2g} \\[0.5em]

Hence, h_max = $\dfrac{u^2}{2g}$