Assertion -Horizontal range is same for angle of projection - and 90- Reason- Horizontal range is independent of angle of projection-

The correct option is C Assertion is correct but Reason is incorrectlet R_1 = R_2 u^2 sin 2θ_1g = u^2 sin 2θ_2g sin 2θ_1 = sin 2θ_2 2θ_1 = ...

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Standard XII

Mathematics

Properties Derived from Trigonometric Identities

Assertion :Ho...

Question

Assertion :Horizontal range is same for angle of projection $θ$ and $(90 - θ)$ . Reason: Horizontal range is independent of angle of projection.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Both Assertion and Reason are incorrect

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Solution

The correct option is C Assertion is correct but Reason is incorrect
let $R_{1} = R_{2}$
$\frac{u^{2} s i n 2 θ_{1}}{g} = \frac{u^{2} s i n 2 θ_{2}}{g}$
$s i n 2 θ_{1} = s i n 2 θ_{2}$
$2 θ_{1} = π - 2 θ_{2}$
$θ_{1} = \frac{π}{2} - θ_{2}$

Range does depend on angle of projection

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Assertion :Horizontal range is same for angle of projection θ and (90−θ). Reason: Horizontal range is independent of angle of projection.

The correct option is C Assertion is correct but Reason is incorrectlet R1=R2u2sin2θ1g=u2sin2θ2gsin2θ1=sin2θ22θ1=π−2θ2θ1=π2−θ2Range does depend on angle of projection

Assertion :Horizontal range is same for angle of projection $θ$ and $(90 - θ)$ . Reason: Horizontal range is independent of angle of projection.

The correct option is C Assertion is correct but Reason is incorrect
let $R_{1} = R_{2}$
$\frac{u^{2} s i n 2 θ_{1}}{g} = \frac{u^{2} s i n 2 θ_{2}}{g}$
$s i n 2 θ_{1} = s i n 2 θ_{2}$
$2 θ_{1} = π - 2 θ_{2}$
$θ_{1} = \frac{π}{2} - θ_{2}$

Range does depend on angle of projection