Overview
This lecture covers key concepts and problem-solving strategies for projectile motion, including independence of motions, use of kinematic equations, and detailed walkthroughs of example problems.
Key Concepts of Projectile Motion
- X (horizontal) and Y (vertical) motions are independent in projectile motion.
- Acceleration due to gravity (g) is 9.8 m/s² downward; set its sign based on your positive direction convention.
- Horizontal acceleration is zero, so horizontal velocity (Vx) is constant.
- Vertical velocity (Vy) is zero at maximum height.
- Kinematic equations are used separately for X and Y directions; only the first equation is used for X since ax=0.
- Delta (Δ) indicates "final minus initial" for any variable.
Problem-Solving Tips
- Always choose and clearly define the origin, and set positive X and Y directions.
- Keep X and Y variables and equations organized; time (t) is the same for both directions at each instant.
- Write out all known and unknown values for both axes before starting.
- If the problem can’t be solved in one step, solve for intermediate variables as needed, often using multiple equations.
Example Problem Walkthroughs
Upward-Thrown Ball
- Initial velocity: 5 m/s upwards from 1.5 m above ground.
- Use kinematic equations to find speed when it hits the ground; final speed ≈ 7.38 m/s.
- Check answers by keeping sufficient decimal places throughout calculations.
Coin Flipped Upwards
- Coin returns to same height after 1 second.
- Use equations for 1D motion; initial vertical speed = 4.9 m/s.
- Time to max height = 0.5 s (half total time), Vy at max height = 0 m/s.
Cannonball Maximum Height (Graph Problem)
- Initial height: 0.5 m, initial Vy: 25 m/s, Vy = 0 at 2.55 s.
- Use kinematic equations to find max height: ≈ 32.3 m.
- Time isn't always necessary if other variables are known.
Horizontally Thrown Ball
- From 8 m height, Vx = 3 m/s.
- Find the impact angle using right triangle trig: tan⁻¹(|Vy/Vx|); result ≈ 76.5°.
Golf Ball Over Fence
- Initial speed: 30 m/s at 60°, fence at 70 m away, 10 m high.
- Find height at x = 70 m using times from X motion; if y > 10 m, ball clears.
- Confirm with both approach methods; both show the ball clears the fence.
Projectile Range (Unknown Initial Speed)
- Ball kicked at 50°, in air for 3 s, starts/ends at ground.
- Calculate Vy using total time, then relate to Vx using tan(θ).
- Find horizontal distance (range): ≈ 37 m.
Key Terms & Definitions
- Projectile Motion — motion of an object under gravity’s influence, moving in two dimensions.
- Kinematic Equations — equations relating displacement, velocity, acceleration, and time.
- Component — the X or Y part of a vector.
- Magnitude — the size or length of a vector, ignoring direction.
Action Items / Next Steps
- Watch lesson videos for the basics of projectile motion if not already completed.
- Practice by solving similar projectile motion problems, organizing variables before starting.
- Check answers by plugging values back into original equations.