Two ships, A and B, leave port at the same time. Ship A travels northwest at 22

Question

Two ships, A and B, leave port at the same time. Ship A travels northwest at 22 knots and ship B travels at 30 knots in a direction 42degree west of south. (1 knot = 1 nautical mile per hour; see Appendix D.) What are (a) the magnitude (in knots) and direction (measured relative to east) of the velocity of ship A relative to B? After how many hours will the ships be 120 nautical miles apart? What will be the bearing of B (the direction of the position of B) relative to A at that time? (For your angles, takes east to be the positive x-direction, and north of east to be a positive angle. The angles are measured from -180 degrees to 180 degrees. Round your angles to the nearest degree.) Number units Number units Number units

Explanation / Answer

a) Vac = Vab + Vbc
22(i + j)/sqroot(2) - 30(-sin(42)i - cos(42)j) = Vab = 35.63i + 37.85j
|Vab| = 51.98241 knots
b) Direction = theta = arctan(37.85/35.63) = 46.730 deg north of east
c) for 120 nautical miles, t = 120/51.98241 = 2.3 hrs
d) Bearing = 226.73 deg

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