Question

Assertion When $θ$ = 45° or 135°, the value of R remains the same, only the sign changes.
Reason $R = \frac{u^{2} \sin 2 θ}{g}$ [AIIMS 2017]

Moderate

A

Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
B

Both Assertion and Reason are correct and Reason is not the correct explanation of Assertion.
C

Assertion is correct but Reason is incorrect.
D

Assertion is incorrect but Reason is correct.

Solution

Horizontal range, $R = \frac{u^{2} \sin 2 θ}{g}$
When $θ$ = 45°, maximum horizontal range,
$R_{\max} = \frac{u^{2}}{g} \sin 90 ° = \frac{u^{2}}{g}$
When $θ$ = 135°, maximum horizontal range,
$R = \frac{u^{2}}{g} \sin 270 ° = \frac{- u^{2}}{g}$
Negative sign implies opposite direction.

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