Question

Statement I: The maximum horizontal range of projectile is proportional to square of velocity.
Statement II:The maximum horizontal range of projectile is equal to maximum height attained by projectile.

• A. If both statement I and statement II are true and statement II is the correct explanation of statement I.
• B. If both statement I and statement II are true but statement II is not the correct explanation of statement I.
• C. If statement I is true but statement II is false.
• D. If both statement I and statement II are false.

Answer 1

Answer: (C)

$R=\frac{u^{2} \sin\, 2\theta}{g}$
$\therefore R_{max} = \frac{u^{2}}{g}$ when $\theta=45^{\circ} $
$\therefore R_{max } \propto u^{2}$
Height $H=\frac{u^{2} \sin^{2} \theta}{2g} $
$\Rightarrow H_{max}=\frac{u^{2}}{2g}$ when $\theta=90^{\circ} $
It is clear that $H_{max} =\frac{R_{max}}{2}$