Final answer:
In high school physics, particularly kinematics, projectile motion and free-fall motion are scenarios where two kinematic equations are required to solve for unknowns when three variables are known.
Step-by-step explanation:
The subject of this question is physics, specifically kinematics, and it pertains to the high school level. In kinematics, solving problems involving motion often requires the use of kinematic equations. These equations relate the five key variables in motion: displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t). When analyzing problems in kinematics, we typically need three known variables to solve for the unknowns using kinematic equations.
Projectile motion and free-fall motion are two scenarios where we often use a pair of kinematic equations to solve for unknown quantities given three known ones. For instance, in projectile motion, if we know the initial velocity, angle of launch, and maximum height achieved by the projectile, we would use one equation to solve for time and another for horizontal range. Similarly, in free-fall motion, if we know the initial height, initial velocity, and acceleration due to gravity, we can use one equation to find the time taken to reach the ground and another to determine the final velocity just before impact.