AP Physics 1 Projectile Motion — AP Physics 1
1. Core Principles of Projectile Motion ★★☆☆☆ ⏱ 4 min
Projectile motion describes the motion of an object (called a projectile) launched into the air, where after launch, the only force acting on it is constant downward gravity (air resistance is always ignored in AP Physics 1 problems). It is assessed in both multiple-choice and free-response sections of the AP exam, often as part of multi-concept problems linking to forces, energy, or momentum.
The foundational principle of projectile motion is that horizontal and vertical motions are completely independent, connected only by the shared time of flight. Gravity acts exclusively vertically, so there is no horizontal acceleration, allowing us to split any 2D problem into two separate 1D kinematics problems.
v_{0x} = v_0 \cos\theta_0 \qquad v_{0y} = v_0 \sin\theta_0
With the standard convention (origin at launch, positive y upward, positive x in direction of motion): acceleration components are $a_x = 0$, $a_y = -g$, where $g = 9.8\ \text{m/s}^2$. The kinematic equations simplify to:
- Horizontal motion: $x = x_0 + v_{0x}t$ (constant velocity)
- Vertical motion: $v_y = v_{0y} - gt$, $y = y_0 + v_{0y}t - \frac{1}{2}gt^2$, $v_y^2 = v_{0y}^2 - 2g(y-y_0)$
Exam tip: Always draw and label your coordinate system explicitly, marking the positive y direction, to eliminate 90% of common sign errors on the AP exam.
2. Projectiles Launched From Level Ground ★★☆☆☆ ⏱ 3 min
When a projectile launches and lands at the same vertical elevation ($y_{final} = y_{initial}$), we can derive simplified expressions for time of flight, maximum height, and range that speed up multiple-choice calculations.
Exam tip: The simplified range formula only works for level ground (equal launch and landing elevation). Never use it for projectiles launched from cliffs or hills unless you confirm elevations are equal.
3. Projectiles Launched From Uneven Elevation ★★★☆☆ ⏱ 4 min
Most non-routine AP Physics 1 projectile problems involve launch and landing at different elevations, such as throwing a ball off a building or launching a projectile at a target on a hill. Simplified level-ground formulas do not apply here, so we always return to the core kinematic equations and solve for time first.
- Write the vertical displacement equation using the known final y position
- Rearrange into standard quadratic form in $t$
- Discard any non-physical negative time solution
- Use the valid positive time to solve for unknown horizontal distance or velocity
Exam tip: If you get two positive solutions for $t$, one corresponds to passing the target y-position on the way up, and the other on the way down. Pick the solution that matches the problem's description of where the projectile lands.
4. AP-Style Concept Check ★★★☆☆ ⏱ 3 min
Common Pitfalls
Why: Students correctly remember vertical velocity is zero at maximum height, but forget horizontal velocity remains constant throughout the entire flight
Why: Students memorize the simplified formula and forget it only applies when launch and landing elevation are equal
Why: Students forget velocity is a vector, and add perpendicular components incorrectly
Why: Students forget to check calculator mode before starting calculations, leading to incorrect numerical results
Why: Students overcomplicate problems and incorrectly assume gravity has a horizontal component
Why: Students encounter conflicting conventions from different sources and forget to adjust all terms consistently