A gun fires a large number of bullets upward. Due to shaking of hands some bullets deviate as much as `1°` from the vertical. The muzzle speed of the gun is `150 m//s` and the height of gun above the ground is negligible. The radius of the head of the person firing the gun is 10cm. You can assume that acceleration due to gravity is nearly constant for heights involved and its value is `g = 10 m//s^(2)`. The gun fires 1000 bullets and they fall uniformly over a circle of radius r. Neglect air resistance. You can use the fact `sin theta ~= theta` when `theta` is small.
(a) Find the approximate value of r. (b) What is the probability that a bullet will fall on the person’s head who is firing?

Answer

(a) `80 m` (b) `1.6 xx 10^(-3)`