The man can row the boat in still water with a speed of 5 m/s. If the river is flowing 2 m/s,...
The man can row the boat in still water with a speed of 5 m/s.
A) If the river is flowing at 2 m/s, determine the speed of the boat.
B) Determine the angle θ he must direct the boat so that it travels from A to B.
Homework Answers
Calculate the angle from the geometry of the figure.
Velocity of the river water in Cartesian vector form is expressed as,
Velocity of the boat in Cartesian vector form is expressed as,
Relative velocity in Cartesian vector form is expressed as,
From the relative velocity equation, we have
Substitute 
for 
, 
for 
, and 
for 
.
By equating the 
and
components, we have
…… (1)
…… (2)
Divide equation (1) by equation (2).
Solve the equation by using bisection method.
Substitute 
for 
.
Hence perform iteration for 
.
Again perform iteration for 
Hence, the value of 
lies in between 
and 
.
Calculate the value of 
by using interpolation between 
and 
.
Therefore, the required angle the boat must be directed is
.
Substitute 
for 
in equation (2).
Therefore, the speed of the boat is
.
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