Answer :
The velocity of a woman is (3i + 18j) m/s with a magnitude of 18.25 m/s and 80.54⁰ from the west.
We need to know about vectors to solve this problem. Velocity is included in vectors because it has magnitude and also direction. Velocity can be determined as the distance traveled divided by time interval. Velocity can be written as
v = vx i + vy j
the magnitude of velocity can be determined as
|v| = √(vx² + vy²)
the angle of the vector from x-axis is
tanθ = vy / vx
From the question above, we know that
vx = ( 3 i )mi/h
vy = ( 18 j ) mi/h
Hence, the velocity relative to the surface water is
v = vx i + vy j
v = (3i + 18j) m/s
the magnitude is
|v| = √(vx² + vy²)
|v| = √(3² + 18²)
|v| = √333
|v| = 18.25 m/s
the direction is
tanθ = vy / vx
tanθ = 18/3 = 6
θ = 80.54⁰
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