Overview
This lecture introduces projectile motion in physics, showing how two one-dimensional motions (horizontal and vertical) combine into a single two-dimensional problem.
Principles of Projectile Motion
- Projectile motion involves both horizontal (X) and vertical (Y) components, treated independently.
- The horizontal velocity (Vx) is constant if air resistance is ignored, meaning no horizontal acceleration.
- The vertical motion (Vy) experiences constant acceleration due to gravity, at −9.8 m/s² near Earth’s surface.
- X and Y velocity components are found by splitting the initial velocity vector into Vx = V·cos(θ) and Vy = V·sin(θ).
Vertical Motion Analysis
- The vertical velocity decreases on the way up, reaches zero at maximum height, then increases downward.
- If the projectile lands at the same height it was launched, the final vertical speed equals the initial but downward.
- The equations of motion for the vertical component include:
- Vy = Voy + at
- Δy = Voy·t + ½a·t²
Horizontal Motion Analysis
- With zero horizontal acceleration: Δx = Vx·t
- The horizontal displacement depends only on Vx and total time of flight.
1D Problem Examples
- A hockey puck slides at 86.6 m/s for 10.0 s: travels 866 m (Δx = Vx·t).
- A baseball thrown straight up at 50.0 m/s:
- Time up = 5.10 s, total air time = 10.2 s, using t = (Vf − Vo)/a.
- Max height = 128 m, using average vertical velocity and time up.
2D Problem Examples
- Baseball hit at 100 m/s at 30° above horizontal:
- Vx = 86.6 m/s, Vy = 50.0 m/s.
- Total flight time = 10.2 s (double the time to max height).
- Max height = 128 m.
- Range (Δx) = 883 m.
- Stone thrown horizontally from a 100 m building at 25 m/s:
- Time to ground = 4.5 s (solve −100 = ½(−9.8)t²).
- Distance from building = 110 m (Δx = Vx·t).
- Arrow shot at 98 m/s at 30° to a building 200 m away:
- Vx = 84.9 m/s, Vy = 49 m/s.
- Time to hit building = 2.36 s (200/84.9).
- Height at impact = 88 m.
Key Terms & Definitions
- Projectile motion — motion of an object influenced only by gravity (vertical) and constant horizontal velocity.
- Vector components — splitting a vector into its horizontal (X) and vertical (Y) parts.
- Range — horizontal distance traveled by a projectile.
- Uniform acceleration — constant acceleration, here due to gravity (−9.8 m/s² down).
Action Items / Next Steps
- Practice splitting velocity into components for different launch angles.
- Solve similar problems changing initial velocity, angle, or height.
- Review 1D kinematic equations and their application to 2D motion.