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Question

# A ship A is moving eastwards with a speed of 20 km/h and a ship B ,50 km south of A is moving northwards with a speed of 20 km/h. Then find the shortest distance between the ships.

A
205 km
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B
252 km
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C
103 km
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D
52 km
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Solution

## The correct option is B 25√2 km−→vA=20^i km/h −→vB=20^j km/h velocity of A w.r.t B is, −−→vAB=−→vA−−→vB −−→vAB=(20 ^i−20 ^j) km/h ∴ tanθ=|−20|20=1 ⇒θ=45∘ ∵ velocity of A w.r.t B is directed along direction AP, so the minimum distance (dmin) occurs where relative velocity of A w.r.t B i.e −−→vAB is ⊥ to B. ⇒ From ΔAPB, α=90∘−θ=45∘ Hence, shortest distance between ships is BP, sinα=BPAB ⇒1√2=BP50 ∴BP=50√2=25√2 km

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