To solve this problem:

The boat travels at 8 m/s east, and the river has a northward current of 5 m/s. These two velocities form a right triangle, with the resultant speed being the hypotenuse of the triangle.

The resultant speed $v_r$ can be calculated using the Pythagorean theorem: $v_r = \sqrt{(v_{\text{east}})^2 + (v_{\text{north}})^2}$

Substitute the given values: $v_r = \sqrt{(8)^2 + (5)^2}$ $v_r = \sqrt{64 + 25} = \sqrt{89}$

Using a calculator: $v_r \approx 9.4 \, \text{m/s}$

Thus, the resultant speed is 9.4 m/s, rounded to the nearest tenth.

Let me know if you'd like further clarification! Here are five related questions to expand your understanding:

1. What would the resultant speed be if the river's current increased to 6 m/s?
2. How long would it take for the boat to cross the river if it is 112 meters wide?
3. How can you find the angle of the resultant velocity relative to the east direction?
4. What happens to the boat’s trajectory if it tries to go directly east without compensating for the current?
5. Can you calculate the displacement of the boat after crossing the river due to the current?

Tip: Always visualize problems like this using a triangle to better understand the relationship between the components!