Answer
(a) $10i$
(b) $10i+10\sqrt 3j$
(c) $20i+10\sqrt 3j$
(d) $26.5mi/h$, N $49.1^{\circ}$ E
Work Step by Step
(a) Given the river flows east at 10mi/h, the velocity of the river as a vector in component form is $\vec {v_r} =10i$
(b) Given the motorboat travel $60^{\circ}$ from the shore at 20mi/h, the velocity of the motorboat relative to the water as a vector in component form is $\vec {v_b} =20cos60^{\circ} i + 20sin60^{\circ} j=10i+10\sqrt 3j$
(c) The true velocity of the motorboat is the sum of the above vectors as $\vec {v_t} =\vec {v_b} +\vec {v_r} =20i+10\sqrt 3j$
(d) The true speed is the modulus of the velocity: $|\vec {v_t} |=\sqrt {(20)^2+(10\sqrt 3)^2}\approx26.5mi/h$,
and direction of the jet with respect to the x-axis is $\theta=tan^{-1}\frac{10\sqrt 3}{20}\approx40.9^{\circ}$ or N $49.1^{\circ}$ E
