Final answer:
The boat ends up approximately 116.95 meters downstream.
Step-by-step explanation:
To find how far downstream the boat ends up, we can use the concept of vector addition. The boat is moving south at a speed of 4.9 m/s, and the river is flowing east at a speed of 2.6 m/s. We can treat the boat's motion as the combination of its southward motion and the eastward motion caused by the river.
Using the Pythagorean theorem, we can calculate the resultant velocity of the boat, which is the hypotenuse of a right triangle formed by the southward and eastward velocities. The resultant velocity is approximately 5.63 m/s.
The distance downstream can be calculated by multiplying the resultant velocity by the time taken to cross the river. Since the width of the river is 102.0 m, the time taken can be found using the equation time = distance / velocity. The time is approximately 18.14 seconds. Therefore, the distance downstream is approximately 102.0 m * (5.63 m/s / 4.9 m/s) = 116.95 m.