Question

A jet of water with a cross-sectional area a is striking against a wall at an angle $\theta$ to the horizontal and rebounds elastically. If the velocity of water jet is v and the density is $\rho ,$ the normal force acting on the wall is

• A. $2av^{2}\rho \,\cos \theta$
• B. $av^{2}\rho \,\cos \theta$
• C. $2av\rho \,\cos \theta$
• D. $av\,\cos \theta$

Answer 1

Answer: (A)

$2av^{2}\rho \,\cos \theta$

Answer 2

The normal force acting on the wall $=$ Rate of - change of momentum of water jet $=m v \cos \theta-(-m v \cos \theta)$ $=2 m v \cos \theta$ $=2$ (volume $\times$ density $) v \cos \theta$ $=2(a v \rho) v \cos \theta=2 a v^{2} \rho \cos \theta$