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Q.

Two cars A and B are moving west to east and south to north respectively, along crossroads. A moves with a speed of 72 kmh-1 and is 500m away from point of intersection of cross roads and B moves with a speed of 54 kmh-1 and is 400 m away from point of intersection of cross roads. Find the shortest distance (in m) between them.

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answer is 20.

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Detailed Solution

θ is the angle made by resultant velocity vector VAB with X-axis. tanθ=VBVA=1520=34---(1) tanθ=x500---(2) from (1) & (2) we get  x=375m AB=OB-OC=400-375=25m Shortest path =BP=BCcosθ=2545=20m
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Two cars A and B are moving west to east and south to north respectively, along crossroads. A moves with a speed of 72 kmh-1 and is 500m away from point of intersection of cross roads and B moves with a speed of 54 kmh-1 and is 400 m away from point of intersection of cross roads. Find the shortest distance (in m) between them.