Answer
N $30^{\circ}$ W
Work Step by Step
Step 1. Given the river flows east at 10mi/h, the velocity of the river as a vector in component form is $\vec {v_r} =10i$
Step 2. Assume the motorboat travel $\theta$ from the shore at 20mi/h, the velocity of the motorboat relative to the water as a vector in component form is $\vec {v_b} =20cos\theta i + 20sin\theta j$
Step 3. The true velocity of the motorboat is the sum of the above vectors as $\vec {v_t} =\vec {v_b} +\vec {v_r} =(20cos\theta+10) i + 20sin\theta j$
Stpe 4. For the boat to arrive directly north, the horizontal component of the above vector need to be zero: $(20cos\theta+10=0$ which gives $\theta=120^{\circ}$ or N $30^{\circ}$ W
