Answer
a. $13.59i+2.34j$
b. $14\ mph$
c. $13.9^\circ$
Work Step by Step
a. Based on the given conditions, we can represent each velocity as a vector. For the boat, we have
$\vec v_1=15i\ cos25^\circ+15j\ sin25^\circ \approx13.59i+6.34j$
For the stream, we have
$\vec v_2=-4j$ (vertically down)
Thus, we can find the vector representing the boat's velocity relative to the ground as
$\vec v=\vec v_1+\vec v_2=13.59i+2.34j$
b. The boat's speed can be found as
$|\vec v|=\sqrt {13.59^2+2.34^2}\approx14\ mph$
c. We can find this angle from
$cos\theta=\frac{13.59}{14}\approx0.97$ and $\theta=cos^{-1}(0.97)\approx13.9^\circ$
