Question

A missile fired from ground level rises $x$ metres vertically upwards in $t$ seconds and $x=t(100-12.5t)$. Then the maximum height reached by the missile is

• A. $100m$
• B. $150m$
• C. $250m$
• D. $200m$

Answer 1

The correct option is D $200m$

Given, $x=t(100-12.5t)$

$\Rightarrow x=-12.5(t^2-8t)$

$\Rightarrow x=-12.5(t^2-8t+16-16)=-12.5\left[\right(t-4{)}^2-16]$

$\Rightarrow x=12.5\times 16-12.5(t-4{)}^2=200-12.5(t-4{)}^2\le 200$

Since $-12.5(t-4{)}^2\le 0\forall t\in R$

Hence maximum height reached by missile is at $t=4$ sec.

$\Rightarrow x=4(100-(12.5\times 4\left)\right)=200m$