$\begin{array}{1 1}(A)\;100m \\(B)\;25 m \\(C)\;300m\\(D)\;2m \end{array} $

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Comparing$y=x -\large\frac{x^2}{100}$

with $y=\tan\theta x-\large\frac{1}{2} \frac{g}{u^2 \cos ^2 \theta}$$x^2$

we get the angle of projection to be $ \theta =45$

Maximum height is given by

$H= \large\frac{v_0^2 \sin ^2 \theta }{g} $

$\quad= \large\frac{1000( 1/ \sqrt 2 )^2}{2(10)}$

$\qquad= 25 m$

Hence B is the correct answer.

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