a bullet traveling horizontally at a speed of 350m/s hits a board perpindicular to the surface,?

Question

Passes through it , and emerges on the other side at a speed of 210m/s. If the board is 4.00cm thick, how long does the bullet take to pass through it?

Answer 1

♣ the board is thick h=v1*t-0.5a*t^2, where deceleration
a=(v1-v2)/t, v1=350 m/s, v2=210 m/s, t is time in question, h=0.04 m;
thus 0.04 = 350*t –(350-210)*t/2,
hence t=2*0.04/(350+210) =0.000143 s;

Answer 2

There is no exact solution, becuse we do not know how the force acting on the bullet depends on its speed.

Lets assume that the board behaves as fluid, and the force is proportional to velocity squared:
F = -kmv².

Then we have
d(KE)/dt = -v kmv² = -kmv³
d(KE)/dt = -k √(8/m) √KE³
d(KE)/√KE³ = -k√(8/m) dt

-2 d(1/√KE) = - k√(8/m) dt
d(1/√KE) = k√(2/m) dt
1/√KE = k√(2/m) t + C
√(2/m) 1/v = k√(2/m) t + C
1/v = kt + C
v = 1/(kt + C)

dx = vdt
x = 1/k ln(kt + C) + A

Now we have four equations for A, C, T and k:
0 = x(0) = 1/k ln(C) + A
h = x(T) = 1/k ln(kT + C) + A
vo = v(0) = 1/C
v1 = v(T) = 1/(kT + C)

C = 1/vo
kT = (vo -v1)/(vov1)
A = 1/k ln(vo)
k = 1/h ln(vo/v1)



Answer:
T = (1/v1 - 1/vo) h ln(vo/v1) = 3.90μs

Answer 3

A reasonable first approximation assuming that the block does not move is :

Average speed of bullet through block = 280m/s =28000cm/s

Time to travel through the block = (4cm+length of bullet in cm)/28000

Bramble

Answer 4

Assuming constant deceleration, mean velocity v = (v0 + v1)/2. Then time = s/v = 2*0.04/(v0 + v1) = 0.000142875 sec.