Fig. 6. Paths of a shot from a gun, trajectories.
What are the various angles to which a gun should be raised in order that it may shoot various distances? ([See Fig. 6.]) (The paths of a shot from a gun are called trajectories.)
If a plane flies in a direction always at the same angle from the north, how much farther will it travel than if it flew along the shortest path? ([See Fig. 7.]) (A path always at the same angle from the north is called a loxodrome, and a shortest path on a globe is called a great circle.)
How should an engine be designed so that it will have the least vibration when it moves fast?
In physical problems like these, the answer is not a single number but a formula. What we want to do in any one of these problems is find a formula so that any one of the quantities may be calculated, given the behavior of the others. For example, here is a familiar problem in which the answer is a formula and not a number:
Fig. 7. Paths of a flight.
Fig. 8. Room formulas.