An ocean liner is heading due north with a speed of 8.5m/srelative to the water.

Question

An ocean liner is heading due north with a speed of 8.5m/srelative to the water.   A small sailboat is heading45o east of north with a speed of 1.0m/s relative to thewater. Find the relative velocity (magnitude and direction)of the sailboat as observed by the passengers on theoceanliner. Determine the directional angle relative to duenorth. answer: 7.8m/s, 174.8o E of N An ocean liner is heading due north with a speed of 8.5m/srelative to the water.   A small sailboat is heading45o east of north with a speed of 1.0m/s relative to thewater. Find the relative velocity (magnitude and direction)of the sailboat as observed by the passengers on theoceanliner. Determine the directional angle relative to duenorth. answer: 7.8m/s, 174.8o E of N

Explanation / Answer

let the unit vector in east direction be i and north directionbe j then
speed of liner relative to water v = 8.5 j speed of sail boat relative to water v ' = 1 * cos 45 i+ 1 * sin 45 j                                                          = 0.7071 i + 0.707 j relative velocity of the sailboat as observed by thepassengers on the oceanliner V = v ' - v                                V = 0.707 i - 7.792 j magnitude V = [ 0.707^2 + -7.792^2 ]                     = 7.824 m / s Let V makes an angle with south then tan = 0.707/ 7.792                                                                   = 5.184 degrees So, angle with north = 180 -                               = 174.8 degrees

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