The question as it appears in the 04/03 edition of Specs & Techs from GlobalSpec:
You are standing 100 m from a 20 m tall building. On the roof of the building you see a burglar. Trying to be a good citizen, you point your BB gun at him. At the moment you pull the trigger, he falls to the ground. Your BB gun shoots at a speed of 60 m/s. Did you hit him?
(Update: April 10, 8:55 AM) And the Answer is...
Yes, at this speed you will catch the burglar.
The following figure lays out the problem:
In this case we have:
In order to hit the burglar two conditions must be met:
1) The range of the BB gun (R in the figure) must be bigger or equal to 100 m
2) The time for the BB gun bullet and the burglar must reach point (c, b) must be equal.
Condition 1: The range of a projectile is given by the equation
where is the initial velocity, is the angle that the bullet leaves the BB gun, and is the acceleration of gravity. From the figure we find that the angle is
Substitute these numbers into the formula for R and get R = 141m.
Then condition 1 is satisfied.
Condition 2:
Let's calculate the time that the projectile (the bullet) reaches the point (c,b) and the time that the burglar (free fall) reaches point (c,b). Let's consider the two cases separately.
(a) Projectile motion:
h = a + b
The motion equations for the horizontal and vertical coordinates are given by
Let be the time the projectile reaches the point (c,b), then these equations become
(1)
(2)
from (1) we get
(3)
Substitute (3) into (2)
or,
and finally,
(4)
(b) Free Fall Motion
The freefall equations are as follows:
(5)
Now, let's be the time that the burglar reaches the point (c,b). Noting that , (5) becomes
(6)
or,
(7)
Now, by comparing equations (4) and (7), we conclude that
Therefore your BB gun will catch the burglar.

Re: Burglars and BBs: Newsletter Challenge (04/03/07)