A river flows southeast at 10 km/hr and a boat floats upon it with its bow pointed in the direction of travel. A man walks upon the deck at 2 km/hr in a direction to the right and perpendicular to the direction of the boat's movement. Find the velocity of the man with respect to the earth.

Question

Accepted Answer

Consider Figure 1.6 as illustrating the problem. The velocity of the boat is

[latex]u_{b}=10\left(\cos 45^{\circ}a_{x}-\sin 45^{\circ}a_{y}\right)=7.071a_{x}-7.071a_{y}km/hr[/latex]

The velocity of the man with respect to the boat (relative velocity) is

[latex]u_{m}=2\left(-\cos 45^{\circ}a_{x}-\sin 45^{\circ}a_{y}\right)=-1.414a_{x}-1.414a_{y}km/hr[/latex]

Thus the absolute velocity of the man is

[latex]u_{ab}=u_{m}+u_{b}=5.657a_{x}-8.485a_{y}[/latex]

[latex]\left|u_{ab}\right|=10.2 \angle{-56.3^{\circ}}[/latex]

that is, 10.2 km/hr at 56.3° south of east.

Question 1.3: A river flows southeast at 10 km/hr and a boat floats upon i...

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