Ship A is located 3.9 km north and 2.7 km east of ship B. Ship A has a velocity

Question

Ship A is located 3.9 km north and 2.7 km east of ship B. Ship A has a velocity of 19 km/h toward the south and ship B has a velocity of 40 km/h in a direction 35° north of east. What are the (a) x-component and (b) y-component of the velocity of A relative to B? (Axis directions are determined by the unit vectors i Overscript EndScripts and j Overscript EndScripts, where i Overscript EndScripts is toward the east.) (c) At what time is the separation between the ships least? (d) What is that least separation?

Explanation / Answer

Va = - 19 j^

Vb = 40 Cos35 i^ + 40 Sin35 j^

Vab = Va - Vb = - 19 j^ - 40 Cos35 i^ - 40 Sin35 j^

Vab = - 40 Cos35 i^ - (40 Sin35 + 19) j^

a)

X-component = - 40 Cos35 = - 32.77 m/s

b)

Y-component = - (40 Sin35 + 19) = - 41.94 m/s

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