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The man can row the boat in still water with a speed of 5 m/s. If the river is flowing 2 m/s,...

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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.

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Answer #1

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 andcomponents, 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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