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BRAINLIEST IF CORRECT: A ferry boat departed from port and traveled at a rate of 10 miles per hour at an angle 30 degrees north of east across a large river.If the current is flowing at a rate of 4 miles per hour straight south, what is the speed and direction of the boat inn the water?

____: miles per hour
____: degrees north of east

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Answer:

Step-by-step explanation:

Relative to the water, the boat is moving

10sin30 = 5 mph N

10cos30 = 8.66 mph E

As the water is flowing 4 mph south, the net boat north velocity is 5 - 4 = 1 mph relative to shore

So relative to shore, the boat appears to be moving

v = √(1² + 8.66²) = √76 = 8.71779... 8.7 mph

θ = arctan(1/8.66) = 6.58677... 6.6° N of E

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