Question

Assertion: When a body is projected at an angle $45^{\circ }$, its range is maximum.
Reason: For maximum of range, the value of $\sin 2\theta$ should be equal to one.

• A. If both Assertion and Reason are true and the Reason is a correct explanation of the Assertion
• B. If both Assertion and Reason are true but Reason is not a correct explanation of the Assertion
• C. If Assertion is true but the Reason is false
• D. If both Assertion and Reason are false

Answer 1

Answer: (A)

At the topmost point vertical component of velocity $=0$
Let time taken to reach the topmost point $=T$, then
$v_y=0u\sin \theta -gT$
$\Rightarrow T=\frac{u\sin \theta }{g}$
$\therefore$ Total time of flight $=2T=\frac{2u\sin \theta }{g}$
$\therefore$ Range, $R=u\cos \theta \times \frac{2u\sin \theta }{g}=\frac{u^2{\sin }^2\theta }{g}$
$\therefore$ For $R$ to be maximum, ${\sin }^2\theta =1$
$\Rightarrow 2\theta =90^{\circ }$
$\Rightarrow \theta =45^{\circ }$