Minimum Distance Between Moving Points

Question

Devanand’s house is $50	ext{ km}$ West of Pradeep’s house. On Sunday morning, at 10 a.m., they leave their respective houses. Under which of the following scenarios, the minimum distance between the two would be $40	ext{ km}$? **Scenario I:** Devanand walks East at a constant speed of $3	ext{ km/h}$ and Pradeep walks South at a constant speed of $4	ext{ km/h}$. **Scenario II:** Devanand walks South at a constant speed of $3	ext{ km/h}$ and Pradeep walks East at a constant speed of $4	ext{

Accepted Answer

A. In Scenario I, distance after $t$ hours $d(t) = \sqrt{(50 - 3t)^2 + (4t)^2} = \sqrt{25t^2 - 300t + 2500}$. Minimum occurs at $t = \frac{300}{50} = 6	ext{ hours}$. $d(6) = \sqrt{25(36) - 300(6) + 2500} = \sqrt{900 - 1800 + 2500} = \sqrt{1600} = 40	ext{ km}$. Scenario I achieves a minimum distance of $40	ext{ km}$.

Answer

Scenario I only

Answer

Scenario II only

Answer

Scenario III only

Answer

Scenario I and II

Answer

None of the above

Minimum Distance Between Moving Points

Explanation

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