Water jet coming out of a stationary horizontal tube at speed v strikes horizontally a massive wall moving in opposite direction with same speed. Water comes to rest relative to wall after striking. Treating A as cross-section of jet and density of water as ρ. Select the correct alternative(s)

Engineering

Physics

Equation of Continuity

Question

force exerted on the wall is 4ρAv²

force exerted on the wall is 2ρAv²

rate of change of kinetic energy of water jet striking the wall is zero.

rate of change of kinetic energy of water jet striking the wall is 8ρAv³

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mass rate of strike $\frac{dm}{dt}$ = A(2v)ρ
Change in velocity during strike = Δv = ${\vec{v}}_{f} - {\vec{v}}_{i}$ = (–v) – (v) = –2v
Thrust force on jet = Δv $\frac{dm}{dt}$ = $\frac{dm}{dt}$ (–2v) = –4ρAv²
Thrust force on wall = – Thrust force on jet = 4ρAv²
$\frac{d (KE)}{dt}$ = $\frac{1}{2} \frac{dm}{dt} (v_{f}^{2}) - \frac{1}{2} \frac{dm}{dt} (v_{i}^{2})$ = $\frac{1}{2} \frac{dm}{dt} [{(- v)}^{2} - v^{2}]$ = 0

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