(Solved): A river flows southeast at \( 10 \mathrm{~km} / \mathrm{hr} \) and a boat floats upon it with its ...

A river flows southeast at \( 10 \mathrm{~km} / \mathrm{hr} \) and a boat floats upon it with its bow pointed in the direction of travel. A man walks upon the deck at \( 2 \mathrm{~km} / \mathrm{hr} \) 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. Explain the followings: a) Why the position vector of the bow has a \( 45^{\circ} \) angle with respect to earth? b) \( u_{b}=10\left(\cos 45^{0} a_{x}-\sin 45^{0} a_{y}\right) \) - explain why the component of \( a_{y} \) is negative? c) \( u_{m}=2\left(-\cos 45^{0} a_{x}-\sin 45^{0} a_{y}\right) \)-. explain why the component of \( a_{x} \) is negative? d) Why the absolute velocity of the man is the summation of \( u_{b} \& u_{m} \) ? e) \( \left|u_{a b}\right|=10.2 \angle-56.3^{0} \ldots \) is it in rectangular form or polar form? f) Can you comment just by looking at the angle of its direction?