B.Sc. maths 3rd yr A bullet fired into a target loses half its velocity after penetrating 1/4 metre.how much further it will penetrate

Question

It a b.sc. level question and it is dynamics question

 

Answer 1

If it loses half of its speed for each 0.25 m of penetration, then its speed obeys the law

 

v(x) = v₀ (1 - 0.5)^x/0.25 = v₀ (0.5)^x/0.25

 

v₀ = speed at which it strikes the target

x = penetration depth in meters

 

Set v(x) = 0 and solve for x.  However, theoretically, it never reaches a speed of zero, although it quickly converges toward zero.  To solve a problem like this realistically, you need to specify a tiny maximum speed close to zero, and solve for the distance to attain that tiny speed.