A boat is traveling across a river that flows due east at 8.50 m/s. The compass
heading of the boat is 15.0°. Relative to the water, the boat is traveling straight
forward (in the direction in which the boat is pointing) at 11.2 m/s. How fast and
which way is the boat moving relative to the banks of the river?
Okay, here we have a situation in which the boat is being carried downstream by the movement
of the water at the same time that it is moving relative to the water. Note the given information
means that if the water was dead still, the boat would be going 11.2 m/s at 15.0° East of North.
The water, however, is not still. Defining
v
to be the velocity of the water relative to the ground,
WG
v
to be the velocity of the boat relative to the water, and
BW
v to be the velocity of the boat relative to the ground; we have
BG
NORTH
v = 11.2 m/s
φ
BW
=
v
BG
15.0°
EAST
θ
v = 8.50 m/s
W G
Solving this problem is just a matter of following the vector addition recipe. First we define +x
to be eastward and +y to be northward. Then we draw the vector addition diagram for v
.
WG
Breaking it up into components is trivial since it lies along the x-axis:
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