Question

A tank, placed on the ground, is filled with water up to a height ℎ. A small hole is made at a height ℎ1 such that ℎ1 < ℎ. The water jet emerging from the hole strikes

the ground at a horizontal distance D, as shown schematically in the figure. Which of the following statements is correct? (g is the acceleration due to gravity)

• A. Velocity at ℎ₁ is \(\sqrt{2𝑔ℎ_1}\)
• B. 𝐷 = 2(ℎ − ℎ1)
• C. D will be maximum when ℎ₁ = \(\frac{2}{3}\) ℎ
• D. The maximum value of D is h

Answer 1

The Correct Option is D

The water jet’s horizontal distance \( D \) from the hole to the point where it strikes the ground depends on the velocity of the jet at height \( h_1 \) and the gravitational pull. The velocity at the hole is given by:

\[ v = \sqrt{2gh_1} \]

This is the velocity of the jet when it leaves the hole at height \( h_1 \), as the velocity is due to the gravitational potential energy being converted into kinetic energy.

Key Observation:

The maximum horizontal distance \( D \) occurs when the jet’s flight time and horizontal speed are maximized.

Conclusion:

The maximum horizontal distance \( D \) is greatest when the height of the hole is maximized, i.e., \( h_1 = h \). Therefore, the maximum value of \( D \) is:

\[ D = h \]

Thus, the maximum value of \( D \) is indeed \( h \).