A boat moves through the water of a river at 5 m/s relative to the water, regardless of the boat's direction. If the water in the river is flowing at 1.6 m/s, how long does it take the boat to make a round trip consisting of a 180 m displacement downstream followed by a 180 m displacement upstream?
To find the time it takes for the boat to make a round trip, we need to consider the relative velocity of the boat with respect to the ground. This can be calculated by adding or subtracting the velocity of the boat with respect to the water and the velocity of the water itself, depending on whether the boat is moving downstream or upstream.
Let's break down the round trip into two parts: the downstream displacement and the upstream displacement.
1. Downstream Displacement:
The boat is moving in the same direction as the water's flow, so we need to add the velocities:
Relative velocity downstream = velocity of the boat + velocity of the water = 5 m/s + 1.6 m/s = 6.6 m/s
The downstream displacement is 180 m, and we can use the formula: Time = Distance / Speed
Time downstream = 180 m / 6.6 m/s ≈ 27.27 seconds
2. Upstream Displacement:
The boat is moving against the water's flow, so we need to subtract the velocities:
Relative velocity upstream = velocity of the boat - velocity of the water = 5 m/s - 1.6 m/s = 3.4 m/s
The upstream displacement is also 180 m:
Time upstream = 180 m / 3.4 m/s ≈ 52.94 seconds
To calculate the total time for the round trip, we need to add the times for the downstream and upstream displacements:
Total time = Time downstream + Time upstream
Total time = 27.27 seconds + 52.94 seconds ≈ 80.21 seconds
Therefore, it takes approximately 80.21 seconds for the boat to make a round trip.