Parametric modelling
Objective. Interpret motion and geometry through a parameter.
- 1. Learn
- 2. Worked example
- 3. Practice
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Learn: the key idea
Parametric modelling uses a parameter, often time, to describe real motion or geometric paths where x and y positions both change together, such as projectile motion with x=ut, y=vt−4.9t². Example: a particle with x=5t, y=10t−5t² reaches the ground when y=0, giving t=2 (ignoring t=0), so its horizontal distance travelled is x=5(2)=10. This approach lets both position coordinates be found simultaneously from a single time value.
Worked example
A projectile's motion is modelled parametrically by x=4t, y=15t−5t². Find the horizontal distance travelled when the projectile lands.
- 1Set y=0 to find landing time: 15t−5t²=0
- 2Factorise: 5t(3−t)=0, so t=0 or t=3
- 3Reject t=0 as the starting point, so landing occurs at t=3
- 4Substitute t=3 into x=4t to find horizontal distance
Answer: 12
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Start practisingCommon mistake. Students solve for t using only the x equation when the context requires the y equation (or vice versa), such as finding landing time from the wrong coordinate; always identify which equation matches the given condition.
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