Chapter 1 - Vectors - 1.2 Length and Angle: The Dot Product - Exercises 1.2 - Page 290: 39

$60^\circ$

We have: the velocity of Bert relative to the water is $2$ms$^{-1}$. We decompose the vector into its components: $$v_{BW}=2\cos\theta\hat{i}+2\sin\theta\hat{j}$$ We have $$v_B=v_{BW}+v_W$$ Bert wants to swim in the shortest path, so his horizontal velocity will be zero: $$v_B=0=2\cos\theta-1$$ So we now have $$\theta = \arccos(\frac{1}{2})=60^\circ$$