Question

A particle is projected at an angle with the horizontal such that it follows a trajectory given by the equation $y=6x-2x^2$. Find the maximum height attained by it.

• A. $4.5m$
• B. $4m$
• C. $3.5m$
• D. $3m$

Answer 1

The correct option is A $4.5m$

If $y=a{x}^2+bx+c$, curve is parabolic in nature and peak occurs at
$x=-\frac{b}{2a}$
If we substitute this $x$ in the expression of $y$ we get maximum height attained by particle
$H_{max}=\frac{4ac-b^2}{4a}$
In expression, $y=6x-2x^2,a=-2$ and $b=6$ and $c=0$
$H_{max}=\frac{-b^2}{4a}=\frac{36}{8}=4.5m$