Review the key concepts, equations, and skills for analyzing horizontally launched projectiles, including how to solve motion problems in two-dimensions using the kinematic formulas.
|Range||The maximum horizontal distance a projectile travels.|
We don't have any new equations, hooray! The equations are the same kinematic formulas as in one dimension, but we now have one set of variables and formulas for each dimension.
Simplifying the horizontal equations
For the horizontal direction, is always zero because gravity does not act in this direction. Thus, the kinematic formulas with terms simplify to:
How to solve motion problems in two-dimensions
- List our known and unknown variables. Note: the only common variable between the motions is time .
- Break the motion into horizontal and vertical components parallel to the - and -axes. Motion in each dimension is independent of the other.
- Solve for the unknowns in the two separate motions—one horizontal and one vertical. We do this using the same procedure as in 1D motion.
Common mistakes and misconceptions
- Some students forget that motion in the - and -direction are independent. What happens in the -direction does not affect the -direction and vice versa.
- Make sure to define the coordinate axes and pay attention to the sign of the acceleration constant . If upward is positive and a ball falling down toward the Earth, is because the acceleration is in the negative direction.
For deeper explanations, see our video on horizontally launched projectiles.
To check your understanding and work toward mastering these concepts, check out the exercise on solving kinematic equations for horizontal projectiles.
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