A boat travels at 15 m/s in a direction 45° east of north for an hour. The boat then turns and travels at 18 m/s in a direction 5° north of east for an hour. What is the magnitude of the boat’s resultant velocity? Round your answer to the nearest whole number.

16 m/s

Explanation:

First, find the displacement in the east direction.

x = (15 m/s sin 45°) (3600 s) + (18 m/s cos 5°) (3600 s)

x = 102,737 m

Next, find the displacement in the north direction.

y = (15 m/s cos 45°) (3600 s) + (18 m/s sin 5°) (3600 s)

y = 43,831 m

Find the magnitude of the displacement.

d = √(x² + y²)

d = √((102,737 m)² + (43,831 m)²)

d = 111,697 m

Finally, find the resultant velocity.

v = d / t

v = (111,697 m) / (7200 s)

v = 15.5 m/s

Rounded to the nearest whole number, the resultant velocity is 16 m/s.

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