$F=m a \Rightarrow a \propto F$
or, $a \propto \sin t$
$\Rightarrow \frac{d v}{d t} \propto \sin t$
$\Rightarrow \int_{0}^{0} d V \propto \int_{0}^{t} \sin t d t$
$V \propto-\cos t+1$
$\int_{0}^{x} d x=\int_{0}^{t}(-\cos t+1) d t$
$x=\sin t-\frac{1}{2} \sin 2 t$
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Reason $R$ : The efficiency of Carnot's engine depends not only on temperature of cold reservoir but it depends on the temperature of hot reservoir too and is given as $\eta=\left(1-\frac{ T _2}{ T _1}\right)$.
In the light of the above statements, choose the correct answer from the options given below
Assertion A :Two identical balls $A$ and $B$ thrown with same velocity '$u$ ' at two different angles with horizontal attained the same range $R$. If $A$ and $B$ reached the maximum height $h_{1}$ and $h_{2}$ respectively, then $R =4 \sqrt{ h _{1} h _{2}}$
Reason R: Product of said heights.
$h _{1} h _{2}=\left(\frac{u^{2} \sin ^{2} \theta}{2 g }\right) \cdot\left(\frac{u^{2} \cos ^{2} \theta}{2 g }\right)$
Choose the $CORRECT$ answer
