A murder

There's a bullet in Salim's head, blood everywhere, and the suspect is a perfectly trained sniper serving in the Salamiya National Defense Forces (SNDF), because such an accurate shot could only performed by Salamiya snipers. The most famous sniper in the SNDF is Moustafa, who the police have arrested and put in jail.

There was a cameraman at the crime scene (when Salim was murdered) though the press did not manage to get any photos except for this one of the road when the crime was over.

The weather was rainy and the rain was falling onto the earth in an oblique path, your job is to determine the wind velocity V V , which will help the police to determine whether Moustafa could have possibly taken the shot.

What was V V ? in m/s

Details And Assumptions

  • The air drag coefficient for the water drop is 0.14 .
  • The air density is 1.255 k g / m 3 1.255 kg/m^3 .
  • The raindrop frontal area 12.45 1 0 6 12.45 *10^{-6} m^2.
  • Its mass is 50 mg.
  • G G =1.1904 rad.
  • The gravitational acceleration constant is 10 m/s.
  • The raindrop velocity is constant (the limit velocity).
  • The drag force is given by F d = 1 2 μ ρ u 2 A F_d =\frac{1}{2} \mu \rho u^2 A A A is the surface area, u u is the velocity of the raindrop relative to the wind.


The answer is 8.51.

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1 solution

Jafar Badour
Jan 9, 2016

m g = 1 2 μ ρ A u 2 mg=\frac{1}{2} \mu \rho A u^2

we get the limit speed from the equation above

the vertical component of the velocity will remain the same so

v = u t a n ( G ) = 2 m g t a n 2 ( G ) ( g ) ρ μ π r 2 v=utan(G)=\sqrt{\frac{2mgtan^2 (G) (g) }{\rho \mu \pi r^2}} =8.51m/s

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