You swim due north across a stream at 3km/hr. The current flows east with a current of 5km/hr. Find your actual velocity as a magnitude and the true directon you are traveling?

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Answer 1 · 2018-03-23T04:28:16

#color(purple)("Magnitude of the resultant vector PR " = r = 5.83 " kmph"#

#color(brown)("Direction of the resultant vector PR " = theta = 0.54^c#

A resultant vector is the combination of two or more single vectors

#"Swimming due north " vec(PS) = 3 " kmph "#

#" East flow current " color(white)( aa)vec(PQ) = 5 " kmph"#

#"Resultant vector " color(white)( aaa)vec(PR) = sqrt((PQ)^2 + (QR)^2) color(red)( " as PS = QR"#

# r = > sqrt(5^2 + 3^2) = 5.83 " kmph"#

Direction of the vector " theta = tan ^-1 ((QR) / (PQ)#

#theta = tan ^-1 (3/5) = tan ^-1 0.6 = 0.54^c#