A missile is fired from the ground level rises $x$ meters vertically upwards in $t \sec$, where $x=100 t-\frac{25}{2} t^2$. The maximum height reached is

Question

A missile is fired from the ground level rises $x$ meters vertically upwards in $t \sec$, where $x=100 t-\frac{25}{2} t^2$. The maximum height reached is, $100 \mathrm{~m}$, $300 \mathrm{~m}$, $200 \mathrm{~m}$, $125 \mathrm{~m}$

MARKS App · Accepted Answer

Hint : $x=100 t-\frac{25}{2} t^2$ $\frac{d x}{d t}=100-25 \mathrm{t}$ for maximum and minimum $\frac{d x}{d t}=0 \Rightarrow t=4 \mathrm{sec}$ $\frac{d^2 x}{d t^2}=-25 < 0$ $\therefore$ at $\mathrm{x}=4$ it will have maixmum height $x_{\max }=100 \times 4-\frac{25}{2} \times 16=400-200=200 \mathrm{~m}$

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