Assumptions Math Example 1

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Example 1

easy
A student models a ball thrown upward with h(t)=20t−5t2h(t) = 20t - 5t^2 (height in metres, time in seconds). List three assumptions embedded in this model.

Solution

  1. 1
    Assumption 1: Air resistance is negligible — the model uses only gravity, not drag forces.
  2. 2
    Assumption 2: Gravity is constant at approximately 1010 m/sÂČ (using g≈10g \approx 10, so 12g=5\frac{1}{2}g = 5).
  3. 3
    Assumption 3: The ball moves vertically only — horizontal motion is not modelled.
  4. 4
    These assumptions simplify the physics to obtain a tractable mathematical model.

Answer

Key assumptions: no air resistance, constant gravity, vertical motion only\text{Key assumptions: no air resistance, constant gravity, vertical motion only}
Every mathematical model rests on assumptions that limit its validity. Identifying assumptions clarifies when the model is accurate and when it breaks down.

About Assumptions

Statements accepted as true without proof that form the starting conditions for a mathematical argument or model.

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More Assumptions Examples

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Example 3 easy

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Example 4 medium

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