Q. Ski Saga Problem?
James Bond is skiing down a snowy slope in an attempt to run off a hostile pursuer. Unfortunately the pursuer has a speed advantage since James is only able to go 20mph and the pursuer is travelling at 25mph. While they are only 1000 feet apart at the beginning, the gap will close in only a few minutes- unless something tips the balance.
James notes that he and his pursuer carry the same kind of rifle and calculate approximately that their masses are about the same. Recalling his elementary physics, he realizes that each time he fires his weapon back at the pursuer his forward momentum and velocity will increase. Alternatively when the pursuer fires his momentum and velocity will decrease.
Each time James fires a round, his adversary fires back. We would like to know how lots of rounds James must fire to assure that his pursuer can't catch up with him. Suppose that all rounds miss their targets otherwise this exercise would terminate.
Let M be the mass of every including the weapon, man, skis, backpack, etc. The mass of every bullet is m, and the muzzle velocity is v. The governing equation is then
20M+ nmv = 25M- nmv so,
2nmv = 5M
Where n is the number of rounds fired.
We would be fond of to solve the problem using the cgs system of units Then
5mph = 223 cps.
Now let M = 10, 000 g, m = 15 g and v = 30, 000 cps. Substituting in we ought to solve
n = (223.104)/(2.15.3×104)
n ≈ 25.
Therefore when each man has fired 25 rounds, the gap between them will stop decreasing and begin to increase, assuring James' escape.