A shotgun fires a large number of pellets upward, with some pellets traveling very nearly vertically and others as much as 1.00 from the vertical. Assume that the initial speed of the pellets is uniformly 150 m/s, and ignore air resistance.
(a) Within what radius from the point of firing will the pellets land?
(b) If there are 1000 pellets, and they fall in a uniform distribution over a circle with the radius calculated in part (a) what is the probability that at least one pellet will fall on the head of the person who fires the shotgun? Assume that his head has a radius of 10 cm.
(c) Air resistance in fact, has several effects. It slows down the rising pellets, decreases their horizontal component of velocity, and limits the speed with which they fall. Which of these effects will tend to make the radius larger than calculated in part (a), and which will tend to make it smaller? What do you think the overall effect of air resistance will be? (The effect of air resistance on a velocity component increases as the magnitude of the component increases.)