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. $2a{v}^2\rho \cos \theta$
• B. $a{v}^2\rho \cos \theta$
• C. $2av\rho \cos \theta$
• D. $av\cos \theta$

Answer 1

Answer: (A)

The normal force acting on the wall $=$ Rate of - change of momentum of water jet
$=mv\cos \theta -(-mv\cos \theta )$
$=2mv\cos \theta$

$=2$ (volume $\times$ density $)v\cos \theta$
$=2(av\rho )v\cos \theta =2a{v}^2\rho \cos \theta$