Question

Assertion: the range of a projectile remains the same for the angle of projections 30° and 60°. Reason: the range does not depend on the angle of projection. Which is correct?

Answer 1

AnSwEr :

Assertion is correct but reason is false

$\rule{150}{0.5}$

ExplanatioN :

• As we know that $\sf{R = \dfrac{u^2Sin2 \theta}{g}}$

• And if we put angle (Ø) as 30° the value of Range comes to be R = u²Sin60°/g

• As when we put angle (Ø) as 60° the value of Range comes to be R = u²sin120°/g

• And also we know that value of sin 60° is √3/2

• And also we know that the value of sin120° and sin60° are √3/2

So, from were we can say that :

• Sin60° = Sin120° . So, Range is equal

• Range depends on the angle

Answer 2

Assertion is correct but reason is wrong.

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Solution:

⏭ Formula of max. horizontal range in projectile motion is given by

$\boxed{\sf{\pink{\large{R=\dfrac{u^2\sin2\theta}{g}}}}}$

• R denotes horizontal range
• u denotes velocity of projection
• g denotes gravitational acceleration
• $\theta$ denotes angle of projection

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⏭ First case (angle of projection = 30°)

$\implies\sf\:R=\dfrac{u^2\sin2(30\degree)}{g}\\ \\ \implies\sf\:R=\dfrac{u^2\sin60°}{g}\\ \\ \implies\sf\:R=\dfrac{\sqrt{3} u^2} {2g}$

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⏭ Second case (angle of projection = 60°)

$\implies\sf\:R'=\dfrac{u^2\sin2(60\degree)}{g}\\ \\ \implies\sf\:R'=\dfrac{u^2\sin120\degree}{9}\\ \\ \implies\sf\:R'=\dfrac{\sqrt{3}u^2}{2g}$

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• sin60° = sin120° = √3/2

✏ R = R' >> Assertion is right.

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✏ As per formula of max. horizontal range, it is clear that Range depends on the angle of projection.

>> Reason is wrong.

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