Expert: Ahmed Salami - 8/26/2010

Question
I need a formula to a hunting problem.  Say a 100000 gram tiger is headed toward me at 8.94 meters per second.  I have a gun with a velocity of 715 meters per second and the bullets weigh 90 grams each.  HOW MANY BULLETS WILL IT TAKE TO FELL THE BEAST?

Answer
Hi Mike,
Consider the effect of a single bullet. Let the tiger have a mass M and an initial velocity V, and a bullet with mass m and velocity v. Also, let us take the direction of movement of the tiger as the positive direction.
The bullet lodges into the tiger on impact and momentum is conserved according to
MV - mv = (M + m)u
u = (MV - mv)/(M + m)
where u is the velocity of the tiger and bullet after impact.
From our figures,
u = (100000*8.94 - 90*715)/(100000 + 90)
  = (894000 - 64350)/100090
  = 829650/100090
  = 8.29 m/s
and of course we see that the tiger slows down.
The effect of a second bullet is given by
(M + m)u - mv = (M + 2m)U
MV - mv - mv = (M + 2m)U
MV - 2mv = (M + 2m)U
and generally for the nth bullet,
MV - nmv = (M + nm)U
U = (MV - nmv)/(M + nm)
we need U to be zero and so,
MV - nmv = 0
MV = nmv
n = MV/mv
 = 100000*8.94/90*715
 = 894000/64350
 = 13.89
It would take 14 bullets to stop the tiger. This is a rather rigorous proof though since we could have just said that the total momentum of the n fired bullets must balance the momentum of the tiger to bring it to a stop and arrive at
MV = nmv

Note that we have assumed here that all a bullet does is lower the speed of the non-accelerating tiger and so the corresponding physics is appropriate. In reality, the actual number of bullets would depend on how good your shooting is but you know that already, dont you?

Regards