Ship A is 10 km due westof ship b . Ship A is heading directly north at a speed of 30 km/h, while ship b is heading in a direction 60^(@)west of north at a speed of 20 km/h .(i)Determine the magnitude of the velocity of ship B relative to ship A .(ii)What will be their distance of closest approach ?

Ship A is 10 km due westof ship b . Ship A is heading directly north a

1.	Ship A is 10 km due westof ship b . Ship A is heading directly north at a speed of 30 km/h, while ship b is heading in a direction 60^(@)west of north at a speed of 20 km/h .(i)Determine the magnitude of the velocity of ship B relative to ship A .(ii)What will be their distance of closest approach ?
Answer» Solution :Velocity of A = 30 KMPH due North`:. V_(A) = 30 hat(j)` Velocity of b = 20 kmph `60^(@)`west of North `:. V_(B) = - 20 SIN 60^(@) + 20 cos 60^(@) = 10 sqrt(3) hat (i) + 10 hat(j)` Velocity of b w.r.t A`= V_(B) - V_(A)` `= - 10 sqrt(3)hat(i) + 10 hat (j) - 30 hat(j) = - 10 sqrt(3)hat (i) - 20 hat(j)` `V_(R) = \| V_(B) - V_(A)\| = sqrt(100 xx 3 + 400) = 10 sqrt(7)`kmph . Shortest distance : In`Delta LE `ANB shortest distance , AN = AB sin `theta` But distance, AB= 10 KM `:. AN = 10 xx (20)/(10sqrt(7)) = (20)/(sqrt(7)) = 7 . 56 km `