For a projectile, the ratio of maximum height reached to the square of flight time is $g=10m{s}^{-2}$

Step 1: Ratio of maximum height and square of flight time:

Maximum height of projectile, $H=\frac{2u^2{sin}^2\theta }{2g}$

Time period of projectile motion, $T^2=\frac{4u^2{sin}^2\theta }{g^2}$

Ratio of maximum hight and square of time:

$\frac{H}{T^2}=\frac{\frac{u^2{sin}^2\theta }{2g}}{\frac{4u^2{sin}^2\theta }{g^2}}$

$\frac{H}{T^2}=\frac{g}{8}=\frac{10}{8}=\frac{5}{4}$

So, ratio of maximum height and square of flight time:

$\frac{5}{4}$