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## AP®︎/College Physics 1

### Course: AP®︎/College Physics 1>Unit 2

Lesson 4: Horizontally launched projectiles

# Horizontally launched projectile review

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.

## Key terms

TermMeaning
RangeThe maximum horizontal distance a projectile travels.

## Equations

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, a, start subscript, x, end subscript is always zero because gravity does not act in this direction. Thus, the kinematic formulas with a, start subscript, x, end subscript terms simplify to:
\begin{aligned}x &= x_0 + v_xt \\\\ v_x &=v_{x0}\end{aligned}

## How to solve motion problems in two-dimensions

1. List our known and unknown variables. Note: the only common variable between the motions is time t.
2. Break the motion into horizontal and vertical components parallel to the x- and y-axes. Motion in each dimension is independent of the other.
3. 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

1. Some students forget that motion in the x- and y-direction are independent. What happens in the x-direction does not affect the y-direction and vice versa.
2. Make sure to define the coordinate axes and pay attention to the sign of the acceleration constant g. If upward is positive and a ball falling down toward the Earth, a, start subscript, y, end subscript is minus, 9, point, 8, start fraction, start text, m, end text, divided by, start text, s, end text, squared, end fraction because the acceleration is in the negative direction.