Question

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

• A. $200m$
• B. $125m$
• C. $160m$
• D. $190m$
• E. $300m$

Answer 1

Answer: (A)

The given equation is
$x=100t-\frac{25}{2}{t}^2$
On differentiating w.r.t. $x,$ we get $\frac{dx}{dt}=100-\frac{25}{2}.(2t)=100-25t$
We know that the velocity of missile is zero at maximum height.
$\therefore$ On putting $\frac{dx}{dt}=0,$
we get $100-25t=0$
$\Rightarrow$ $t=4$
$\therefore$ $x=100\times 4-\frac{25\times 16}{2}=400-200$
$=200m$