Calculating Force on a Man from Variable Mass Water Jet

[itay2424]

Homework Statement

Water with mass density ρ are being shoot from a jet with cross sectional area A and velocity v0 at a man with mass m0.
1. Find the force acting on a man at rest (assume all the water are absorbed in the clothes)
2. Find the force acting on a man escaping at velocity v<v0.

Homework Equations

dp/dt=ƩF

The Attempt at a Solution

I calculated the momentum of a small water element dm = dmv0.
this is the same as the momentum of the water and the man after the water hits him(no external forces):
dmv0=(m0+dm)v
v=(dmv0)/(m0+dm)

The momentum of the man only after the water hit him is: dp=m0dmv0/(m0+dm).
dp/dt=m0*(dm/dt)*v0/(mo+dm)=ƩF

But i couldn't get an expression of the force without dm or dt.
Thanks for the helpers!

 

[tiny-tim]

welcome to pf!

hi itay2424! welcome to pf!

(try using the X₂ button just above the Reply box )

Water with mass density ρ are being shoot from a jet with cross sectional area A and velocity v0 …

why are you using dm ?

the rate of momentum hitting the man can be calulated from ρ A and v_o

 

[itay2424]

ok, so I replace dm with ρAv₀dt. I still have the same problem.

 

[tiny-tim]

force = rate of change of momentum …

what's the problem? ​

 

[itay2424]

The problem is that I know the rate of change of mass but not the rate of change of velocity.
Edit: nevermind I think I got it.