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}=0 u\, \sin \,\theta-g T $
$\Rightarrow T=\frac{u \,\sin \,\theta}{g}$
$\therefore $ Total time of flight $=2 T=\frac{2 u \sin \theta}{g}$
$\therefore $ Range, $R=u \cos \theta \times \frac{2 u \sin \theta}{g}=\frac{u^{2} \sin ^{2} \theta}{g}$
$\therefore $ For $R$ to be maximum, $\sin ^{2} \theta=1$
$\Rightarrow 2 \theta=90^{\circ} $
$\Rightarrow \theta=45^{\circ}$