Q55 / 155 · WBJEE 2023 · Mathematics
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
- A\(100 \mathrm{~m}\)
- B\(300 \mathrm{~m}\)
- Correct answerC\(200 \mathrm{~m}\)
- D\(125 \mathrm{~m}\)
Solution
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
\(x_{\max }=100 \times 4-\frac{25}{2} \times 16=400-200=200 \mathrm{~m}\)
Hence, the correct answer is option: 'C'.