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Ship A travels due east at 20 km/h. Ship B heads in the direction 37° north of east. If ship B always remains due north of ship A (i.e., the same east coordinate), what is the speed of ship B?

1. 25 km/h
2. 12.5 km/h
3. 50 km/h
4. 33.3 km/h

Correct answer: 25 km/h

Solution

For ship B to always remain due north of ship A, both ships must have the same eastward velocity component at all times. Ship A's eastward velocity = 20 km/h. Ship B travels at angle 37° north of east (i.e., angle 37° from east towards north), so B's eastward component = v_B * cos(37°) = v_B * (4/5). Setting equal: v_B * (4/5) = 20 => v_B = 25 km/h.

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