A car travelling around a banked (tilted) highway turn goes out of control, leaves the road, travels through the air, and lands on the ground a distance (d) from the launch-point, after dropping a certain distance (h) below that point. (A sports equivalent would be a ski jumper taking off at an angle θ above the horizontal.) An investigator needs three pieces of information in order to make a model of the trajectory, mostly for the purpose of finding the initial speed of the car. Why are three pieces of data needed and not two, four, or some other number?

A car travelling around a banked (tilted) highway turn goes out of control, leaves the road, travels through the air, and lands on the ground a distance (d) from the launch-point, after dropping a certain distance (h) below that point. (A sports equivalent would be a ski jumper taking off at an angle θ above the horizontal.) An investigator needs three pieces of information in order to make a model of the trajectory, mostly for the purpose of finding the initial speed of the car. Why are three pieces of data needed and not two, four, or some other number?

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