Q. It is foolish of me to wonder about the physics of a movie that contains skull-piercing carrots and bullet-propelled merry-go-rounds, but in "Shoot 'em Up" would there be any point to shooting down at Mr. Smith when he is falling from the plane? He should be traveling at terminal velocity and wouldn't the bullets also be going that fast, too? Hence, they couldn't catch him?
Alex Kincade, St. Joseph, Mich.
A. According to Hypertextbook.com, "If an object falls with a larger surface area perpendicular to the direction of motion, it will experience a greater force and a smaller terminal velocity. On the other hand, if the object fell with a smaller surface area perpendicular to the direction of motion, it will experience a smaller force and a greater terminal velocity." A skydiver has a larger surface area than a bullet; also, the skydiver is falling, but the bullet is propelled by an explosive charge.
While certainly the cross-sectional geometry would dictate a amount of drag force exerted on the object, one also cannot ignore the mass of the object here, no? For example, take 2 object of the same shape by different mass. While they would fall at the same rate in vacuum, the one with the large mass has a larger gravitational force, and requires a larger drag force (i.e. at a higher velocity) to cause it to reach a terminal velocity.
But the other aspect of it is also interesting. While it is true that the bullet was propelled out of the gun (i.e. initial velocity is some value) while the person fell out of the plane (initial velocity is approximately zero), would the bullet still reaches the same terminal velocity? I say it would, because if it is moving faster than the terminal velocity, the drag force is larger than the gravitational force on it, and will slow it down until they both are equal. So whether the bullet will catch up to the person or not depends how far that person has started his fall.
In other words, what happened as described in the movie isn't impossible physically. But it isn't necessarily what can happen all the time since a few other facts are involved.
So what do you think? Did I analyze this correctly myself?