please need the solution for : A bullet passes through a piece of wood 5 cm thic

Question

please need the solution for : A bullet passes through a piece of wood 5 cm thick. It enters the wood at 250 mt/sec and leaves at 100 mt/sec. It is assumed that the declaration of the bullet, while in the wood, is proportional to the square of its velocity.

a) GIVE a DE for the velocity of the bullet(while in the wood), then solve it.

b) How long does it take the bullet to pass through the wood? ( neglect the lenght of bullet).

c) What minimun thickness of wood will stop the bullet?

d) Is this a realistic model? explain

Explanation / Answer

Assuming constant acceleration we can use the kinematic eqn v^2 = v0^2 + 2*a*delta x to solve for a

a = (v^2 -v0^2)/(2*delta x) = (100^2 - 250^2)/(2*0.5) = -5.25x10^4m/s^2

b) For the time use v = v0 + a*t or t = (v - v0)/a = (100-250)/(-5.25x10^4) = 2.85x10^-3 s = 2.85m/s

c) To stop the bullet use v^2 = v0^2 +2*a*x and solve for x (Note here v =0)

So x = -v0^2/(2*a) = -(250^2)/(2*(-5.25x10^4)) = 0.5952 m = 59.52 cm

there is no bullet that has a velocity of 250 metres a second so all your calculations are compromised, not realistic

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