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Q.
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
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 $