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 1.3 m/s, how long does it take the boat to make a round trip consisting of a 215 m displacement downstream followed by a 215 m displacement upstream?

Question

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 1.3 m/s, how long does it take the boat to make a round trip consisting of a 215 m displacement downstream followed by a 215 m displacement upstream?

So there are two scenarios:

1. Upstream: speed of boat
: 5m/s - 1.3m/s

2. Downstream: speed of boat: 5m/s+1.3m/s

I then multiplied each by 215m and then added that answer, but I get a really small number. I know I am doing something wrong.

Answer 1

sorry i posted this twice!

Answer 2

You're on the right track with your two scenarios for the upstream and downstream speeds. However, instead of multiplying the speeds by the distance and adding the answers, you need to divide the distance by the speed to find the time taken for each segment of the trip.

Let's go through the calculations step by step:

1. Upstream:
Relative speed of the boat = 5 m/s - 1.3 m/s = 3.7 m/s
Distance = 215 m

Time taken for the upstream trip = Distance / Relative speed = 215 m / 3.7 m/s ≈ 58.11 seconds

2. Downstream:
Relative speed of the boat = 5 m/s + 1.3 m/s = 6.3 m/s
Distance = 215 m

Time taken for the downstream trip = Distance / Relative speed = 215 m / 6.3 m/s ≈ 34.13 seconds

Now, to find the total time taken for the round trip, you need to add the time taken for the upstream and downstream segments:

Total time taken = Time taken for upstream trip + Time taken for downstream trip
≈ 58.11 seconds + 34.13 seconds
≈ 92.24 seconds

So, it takes approximately 92.24 seconds for the boat to make a round trip consisting of a 215 m displacement downstream followed by a 215 m displacement upstream.