Water jet is projected at an angle to the horizontal. At the point of projection, the area of the jet is S1 and at the highest point, the area of the jet is S2. The initial velocity of projection is u.

Engineering

Physics

Projectile Motion

BernoulIis Equation and Equation of Continuity

Question

Water jet is projected at an angle to the horizontal. At the point of projection, the area of the jet is S₁ and at the highest point, the area of the jet is S₂. The initial velocity of projection is u.

The rate of volume flow is S₂u.

The range on the level ground is $\frac{2 u^{2}}{g} \frac{S_{1}}{S_{2}} \sqrt{1 - \frac{S_{1}^{2}}{S_{2}^{2}}}$ .

The maximum height reached from the ground is $\frac{u^{2}}{2 g} (1 - \frac{S_{1}^{2}}{S_{2}^{2}})$ .

The angle of projection is $\cos^{- 1} (\frac{S_{1}}{S_{2}})$ .

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S₁ × u = S₂ × u cos θ

$cosθ = \frac{S_{1}}{S_{2}}$

$R = \frac{2 u^{2} sinθcosθ}{g} = \frac{2 u^{2}}{g} \times \frac{S_{1}}{S_{2}} \times \sqrt{1 - \frac{S_{1}^{2}}{S_{2}^{2}}}$

$h_{\max} = \frac{u^{2} \sin^{2} θ}{2 g} = \frac{u^{2}}{2 g} \times (1 - \frac{S_{1}^{2}}{S_{2}^{2}})$ .