Q.

Ship A is moving with velocity 30m/s due east and ship B with velocity 40m/s due north. Initial separation between the ships is 10km as shown in figure. After what time (in seconds) ships are closest to each other ?

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answer is 0120.00.

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Detailed Solution

Velocity toward east,  V→A=30i^ m/sVelocity towards North  V→B=40j^ m/sDistance AB=10 kmV→BA=40j^−30i^V→BA=402+−302=50 m/s⇒tanθ=43;V→BA=50 m/sRequired time==ABcosθVBAt=104×3550=300025=120s
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Ship A is moving with velocity 30m/s due east and ship B with velocity 40m/s due north. Initial separation between the ships is 10km as shown in figure. After what time (in seconds) ships are closest to each other ?