Question

Given below are two statements. One is labelled as Assertion $A$ and the other is labelled as Reason $R$.
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. $h_1{h}_2=\left(\frac{u^2{\sin }^2\theta }{2g}\right)\cdot \left(\frac{u^2{\cos }^2\theta }{2g}\right)$
Choose the CORRECT answer :

• A. Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
• B. Both $A$ and $R$ are true but $R$ is NOT the correct explanation of $A$.
• C. $A$ is true but $R$ is false
• D. $A$ is false but $R$ is true

Answer 1

Answer: (A)

$h_1=\frac{u^2{\sin }^2{\theta }_1}{2g}{h}_2=\frac{u^2{\sin }^2{\theta }_2}{2g}$
$h_1{h}_2=\frac{u^2{\sin }^2{\theta }_1}{2g}\times \frac{u^2{\sin }^2{\theta }_2}{2g}$
${\theta }_2=90-{\theta }_1$
$h_1{h}_2=\frac{u^2{\sin }^2{\theta }_1}{2g}\cdot \frac{u^2{\cos }^2{\theta }_1}{2g}$
$={\left[\frac{u^2\sin {\theta }_1\cos {\theta }_1}{2g}\right]}^2$
$={\left[\frac{u^2\sin {\theta }_1\cos {\theta }_1}{2g}\times \frac{2}{2}\right]}^2=\frac{R^2}{16}$
$R=4\sqrt{h_1{h}_2}$
So R is correct explanation of A