Using Elementary Mechanics to Estimate the Maximum Range of ICBMs Available to Purchase

North Korea’s development of nuclear weapons and, more recently, intercontinental ballistic missiles (ICBMs) has added a grave threat to world order. The threat presented by these weapons depends critically on missile range, i.e., the ability to reach North America or Europe while carrying a nuclear warhead. Using the limited information available from near-vertical test flights, how do arms control experts estimate the maximum range of an ICBM? The purpose of this paper is to show, using mathematics and concepts appropriate to a first-year calculus-based mechanics class, how a missile’s range can be estimated from the (observable) altitude attained during its test flights. This topic—while grim—affords an ideal opportunity to show students how the application of basic physical principles can inform and influence public policy. For students who are already familiar with Kepler’s laws, it should be possible to present in a single class period.