WBJEE 2024 Physics & Chemistry Paper

Here we will use the Bernoulli's equation, and the concept of horizontal projectile motion.
By Bernoulli's equation at point (1) and (2),
‌P1+‌

1

2

ρv12+ρgH1=P2+‌

1

2

ρv22+ρgH2
‌⇒p‌atm ‌+0+ρgH=p‌atm ‌+‌

1

2

ρv2+ρgz
‌⇒v2=2g(H−z)...(1)
By projectile motion,
‌R=v×t⇒t=‌

R

v

‌−z=−‌

1

2

gt2
‌⇒z=‌

1

2

g‌

R2

v2

‌⇒R2=‌

2′zv2

g

‌⇒R2=‌

2z×2g(H−z)

−g

‌ [from eq. (i)] ‌
‌⇒R2=4z(H−z)

By taking derivative with respect to z,
‌⇒2R‌

dR

dz

=4z(−1)+(H−z)4
‌⇒‌

dR

dz

=‌

4H−8z

2R

‌⇒‌

dR

dz

=0⇒4H−8z=0⇒z=‌

H

2