Final answer:
The speed of the boat relative to a stationary shore observer is found by adding the squared boat and current speeds and taking the square root. The boat's downstream displacement upon reaching the opposite shore is determined by calculating the crossing time using the boat's speed and multiplying by the current speed.
Step-by-step explanation:
The question involves the concept of relative velocity from Physics. To find the magnitude of the speed of the boat relative to a stationary shore observer, we use the Pythagorean theorem. Given that the speed of the boat relative to the water is 1.69 m/s and the speed of the current is 0.756 m/s, the total speed relative to the shore, Vtot, is calculated using Vtot = √(v_boat^2 + v_current^2). Thus, Vtot = √(1.69^2 + 0.756^2) m/s.
To determine how far downstream the boat will be from its initial position upon reaching the other shore, we need to consider the time it takes to cross the river and the velocity of the current. The time to cross is time = width/speed = 229 m / 1.69 m/s, and then the downstream distance is downstream distance = time * current speed.