Ship A is located 3.2 km north and 2.1 km east of ship B . Ship A has a velocity
ID: 2140516 • Letter: S
Question
Ship A is located 3.2 km north and 2.1 km east of ship B. Ship A has a velocity of 22 km/h toward the south and ship B has a velocity of 40 km/h in a direction 37
Ship A is located 3.2 km north and 2.1 km east of ship B. Ship A has a velocity of 22 km/h toward the south and ship B has a velocity of 40 km/h in a direction 37 degree north of east. What is the velocity of A relative to B (Express your answer in terms of the unit vectors and , where is toward the east.) Write an expression (in terms of and ) for the position of A relative to B as a function of t, where t = 0 when the ships are in the positions described as above. At what time is the separation between the ships least? What is that least separation?Explanation / Answer
The position vector of
A = (2.4, 4.7) + t(22cos(-90), 22sin(-90))
B = (0, 0) + t(40cos37, 40sin37)
The distance vector from A to B = vector B - vector A =
d = (2.4, 4.7) + t(0-40cos37, 22sin(-90)-40sin37)
d = (2.4, 4.7) + t(-31.945, -46.07)
or d = (2.4 - 31.945t)i + (4.7 - 46.07t)j
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the distance is
d = sqrt(2.4 - 31.945t)^2 + (4.7 - 46.07t)^2) ---> find the minimum: set derivative = 0
d' = (-11727880 + 125717117t)/40 000d > set = 0
t(min) = 0.0932879 h
d(min) = 0.70589 km
Minimum distance = 0.706 km at t = 0.093 h
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