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Inversely Proportional

A ship A is m...

Question

A ship A is moving westwards with a speed of $10 k m h^{- 1}$ and a ship B 100 km south of A, is moving northwards with a speed of $10 k m h^{- 1}$ . Find the time after which the distance between them becomes shortest.

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Solution

$| {\to V}_{A} - {\to V}_{B} | = 10 \sqrt{2} m / s$
With respect to ship B, ship A will be moving along AC with this velocity and the distance between them will become shortest when ship A is at C.
Time taken $= \frac{A C}{| {\to V}_{A} - {\to V}_{B} |} = \frac{100 c o s 45^{\circ}}{10 \sqrt{2}}$
$= 5 h$

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A ship A is moving westwards with a speed of 10 km h−1 and a ship B 100 km south of A, is moving northwards with a speed of 10 km h−1. Find the time after which the distance between them becomes shortest.

|→VA−→VB|=10√2m/s With respect to ship B, ship A will be moving along AC with this velocity and the distance between them will become shortest when ship A is at C. Time taken =AC|→VA−→VB|=100 cos45∘10√2 =5 h

A ship A is moving westwards with a speed of $10 k m h^{- 1}$ and a ship B 100 km south of A, is moving northwards with a speed of $10 k m h^{- 1}$ . Find the time after which the distance between them becomes shortest.