The captain of a boat wants to travel directly across a river that flows due eas

Question

The captain of a boat wants to travel directly across a river that flows due east. He starts from the south bank of the river and heads toward the north bank. The boat has a speed of 5.50 m/s with respect to the water. The captain steers the boat in the direction 330 degrees. How fast is the water flowing? Note that 90 degrees is east, 180 is south, 270 is west, and 360 is north. A) 2.70 m/s B) 2.75 m/s C) 2.85 m/s D) 2.72 m/s The captain of a boat wants to travel directly across a river that flows due east. He starts from the south bank of the river and heads toward the north bank. The boat has a speed of 5.50 m/s with respect to the water. The captain steers the boat in the direction 330 degrees. How fast is the water flowing? Note that 90 degrees is east, 180 is south, 270 is west, and 360 is north. A) 2.70 m/s B) 2.75 m/s C) 2.85 m/s D) 2.72 m/s A) 2.70 m/s B) 2.75 m/s C) 2.85 m/s D) 2.72 m/s

Explanation / Answer

The captain heading is 30° west due to North. According to the vector rule, velocity can be found out by as the sum of two perpendicular components vector.

Here the boat speed is the northward components ( V cosA) and a westward components (V sinA). Also, the westward components of velocity must be equal and opposite to the eastward speed of water.

Here,

V = Actual speed of the boat with respect to the water.

A = Angle between the boats heading and true north.

The boat westward speed is given by

= 5.5 x Sin 30°

= 2.75 m/s

Hence B) is correct answer.

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