Daniel B. answered • 06/03/21
A retired computer professional to teach math, physics
The answer is the vector sum of all the velocities.
It is convenient to calculate the x-y coordinates of all the velocities,
because all the x-coordinates can be added together, and
all the y-coordinates can be added together.
Express the situation in a coordinate system, where East and North are positive.
I do not know what notation you use in school, so I will use two notations:
(x,y) = xi + yj
The man is walking with velocity (-4, 0) = -4i.
The propeller drives the boat with velocity (-15√2/2, 15√2/2) = -15√2i/2 + 15√2j/2.
The tide and wind drive the ship with velocity (0, -5) = -5j
The sum of all the vectors is
(-4 - 15√2/2, -5 + 15√2/2) = -4i - 15√2i/2 - 5j + 15√2j/2
The x-coordinate < 0 and the y-coordinate > 0.
Therefore the resulting velocity is in the second quadrant,
making it somewhere between West and North-West.
The speed is
√((-4 - 15√2/2)² + (-5 + 15√2/2)²) =
√(16 + 60√2 + 225/2) + (25 - 75√2 + 225/2) =
√(266 - 15√2) = 15.6 km/h
