Two snips. A and S leave port at the same time. Ship A travels northwest at 21 k

Question

Two snips. A and S leave port at the same time. Ship A travels northwest at 21 knots and ship B travels at 26 knots in a direction 33west of south 1 knot nautical mile per hour, see Apper D what are (a) the magnitude in knots and b) direct on measured relative to east) of the velocity of ship A relaive to B? (c) After how many hours will the ships be 120 nautical mles apart? (d) What will be the bearing of B (the direction of the position of 6) relative to A at that time? (For your angles, takes east to be the positive x-direction and north of east to be a positlve angle. The angles are measured from -180 degrees to 180 degrees. Round your angles to the nearest degree.) ) Numher (b) Number (c) Number (d) Number

Explanation / Answer

vA = 21 ( - cos45i - sin45j)

vA = - 14.85 i - 14.85j knots

vB = 28 ( - sin33 i - cos33 j)

vB = - 15.25 i - 23.48 j knots

(A) vA/B =vA - vB

= 0.4i + 8.63 j

magniude = sqrt(0.4^2 + 8.63^2)

= 8.64 knots

(B) theta = tan^-1(8.63 / 0.4)

= 87.3 deg

(C) d = v t

120 = 8.64 t

t = 13.9 hrs

(D) theta =- 180 + 87.3

= - 92.7 deg

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