Example ① Projectile motion: the trajectory given by x = v₀ cosα · t, y = v₀ sinα · t − (g/2)t².
Solution: Substitute t = x/(v₀cosα) → y = (tanα)x − (g/(2v₀²cos²α))x²
This is a downward-opening parabola.
Solution: Substitute t = x/(v₀cosα) → y = (tanα)x − (g/(2v₀²cos²α))x²
This is a downward-opening parabola.
Key Point
- Parametric representations work well with physical phenomena such as motion.
Practice Problems
- Eliminate t from x=t² and y=2t.
Solutions and Explanations
- Solution: y² = 4x (a parabola)