Final answer:
The boat takes 68.88 seconds to make a round trip consisting of a 260 m displacement downstream followed by a 260 m displacement upstream in a river with a flow of 1.9 m/s.
Step-by-step explanation:
To calculate the time it takes for the boat to make a round trip in the river, we need to consider the boat's velocity relative to the river and the displacement downstream and upstream.
Since the boat's velocity relative to the water is 8 m/s and the water is flowing at 1.9 m/s, we can calculate the boat's velocity relative to the ground by adding the two velocities. The boat's velocity relative to the ground will be 8 m/s + 1.9 m/s = 9.9 m/s.
To calculate the time for the downstream and upstream displacements, we can use the equation time = distance / velocity. The downstream displacement is 260 m and the velocity relative to the ground is 9.9 m/s, so the time for the downstream displacement is 260 m / 9.9 m/s = 26.26 seconds. The upstream displacement is also 260 m, but since the boat is moving against the current, the velocity relative to the ground will be 8 m/s - 1.9 m/s = 6.1 m/s. Therefore, the time for the upstream displacement is 260 m / 6.1 m/s = 42.62 seconds. To calculate the total time for the round trip, we add the time for the downstream and upstream displacements: 26.26 seconds + 42.62 seconds = 68.88 seconds.