A person can throw a ball upto a maximum range of 100m . How high...

Horizontal range is maximum if the angle of projection is $45 °$ and is given by {R}_\max = \dfrac{{u}^{2}}{g}

Here, {R}_\max = 100m

Then, $100 = \dfrac{{u}^{2}}{g} ⋯ \left(1\right)$

If the ball is thrown vertically upward, then the ball will attain the maximum height from the ground as {H}_\max = \dfrac{{u}^{2}}{2g}

{H}_\max = \dfrac{100}{2} = 50m