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Q.

(A) : For projection angle tan^-1 (4), the horizontal range and the maximum height of a projectile are equal.
(R) : The maximum range of projectile is directly proportional to square of velocity and inversely proportional to acceleration due to gravity.

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a

(A) is true but (R) is false

b

Both (A) and (R) are true and (R) is the correct explanation of (A)

c

Both (A) and (R) are false

d

Both (A) and (R) are true and (R) is not the correct explanation of (A)

answer is B.

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Detailed Solution

$R = \frac{u^{2} \sin 2 θ}{g}$ ; $H_{max} = \frac{u^{2} \sin^{2} θ}{2 g}$

$R = H_{max}$

$\Rightarrow \frac{2 u^{2} sinθcosθ}{g} = \frac{u^{2} \sin^{2} θ}{2 g}$

$\Rightarrow θ = \tan^{- 1} 4$

$R_{\max} = \frac{u^{2}}{g}$

Both (A) and (R) are true and (R) is not the correct explanation of (A).

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(A) : For projection angle tan-1 (4), the horizontal range and the maximum height of a projectile are equal.(R) : The maximum range of projectile is directly proportional to square of velocity and inversely proportional to acceleration due to gravity.