Verified Solution • 2025–26 Session moderate

QJEEAdv22Ph3665: JEE Advanced 2022 Physics - Class 11 JEEAdv22Ph3665 Solution: A projectile is fired from horizontal ground with speed and…

A projectile is fired from horizontal ground with speed vv and projection angle θ\theta . When the acceleration due to gravity is gg , the range of the projectile is dd . If at the highest point in its trajectory, the projectile enters a different region where the effective acceleration due to gravity is g′=g0.81g^{\prime}=\frac{g}{0.81} , then the new range is d′=ndd^{\prime}=n d . The value of nn is ___________ .

Step-by-Step Verified Solution

d=u2sin⁡2θgd=\frac{u^{2} \sin 2 \theta}{g}

H=u2sin2⁡θ2g

So, after entering in the new region, time taken by projectile to reach ground

t=2Hg′=2u2sin2⁡θ×0.812g×g=0.94sin⁡θg

So, horizontal displacement done by the projectile in new region is

x=0.9usin⁡θg×ucos⁡θ

x=0.9usin⁡θg×u=0.9u2sin⁡2θ2g

So, d′=d2+xd^{\prime}=\frac{d}{2}+x

=0.95d

So, n=0.95dn=0.95 d

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