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.
215/(5-1.3) = 58.1sec. upstream
215/(5+1.3) = 34.1 sec. downstream
Round trip time = 92.2 sec.
Well, it seems like you're not doing anything particularly wrong, except for maybe the calculation at the end. Let me help you out with that.
To determine the time it takes for the boat to make a round trip, we need to calculate the time it takes for the boat to go downstream and the time it takes to go upstream, and then add them together.
Let's start with the downstream displacement of 215m. The boat's speed relative to the water is 5m/s, and the water in the river is flowing at 1.3m/s. So, the speed of the boat relative to the river is 5m/s + 1.3m/s = 6.3m/s.
To find the time it takes to go downstream, we divide the distance by the speed:
Time downstream = Distance / Speed = 215m / 6.3m/s = approximately 34.13s
Now let's move on to the upstream displacement of 215m. The boat's speed relative to the water is still 5m/s, but now we need to subtract the speed of the river, which is 1.3m/s, to get the speed of the boat relative to the river:
Speed of boat relative to river = 5m/s - 1.3m/s = 3.7m/s
To find the time it takes to go upstream, we divide the distance by the speed:
Time upstream = Distance / Speed = 215m / 3.7m/s = approximately 58.11s
Finally, to find the total time for the round trip, we add the time downstream and the time upstream:
Total time = Time downstream + Time upstream = 34.13s + 58.11s = approximately 92.24s
So, it takes the boat approximately 92.24 seconds to make the round trip consisting of a 215m displacement downstream followed by a 215m displacement upstream.
I hope this helps, and remember, even if the numbers seem small, they can still make a big difference in calculations!
To calculate the time it takes for the boat to make the round trip, we need to find the time taken for both the downstream and upstream displacements separately.
Let's start with the downstream displacement:
Speed of the boat downstream = Speed of the boat + Speed of the water = 5 m/s + 1.3 m/s = 6.3 m/s
Distance downstream = 215 m
Time taken downstream = Distance downstream / Speed downstream = 215 m / 6.3 m/s
Now let's calculate the time taken for the boat to travel upstream:
Speed of the boat upstream = Speed of the boat - Speed of the water = 5 m/s - 1.3 m/s = 3.7 m/s
Distance upstream = 215 m
Time taken upstream = Distance upstream / Speed upstream = 215 m / 3.7 m/s
Finally, to find the total time for the round trip, we need to add the time taken downstream and the time taken upstream:
Total time taken = Time taken downstream + Time taken upstream
Now you can calculate the total time taken for the round trip by substituting the values into the equation.
You're on the right track with considering the different speeds of the boat relative to the water for the upstream and downstream journeys. However, there's an error in your calculation.
To find the time it takes for the boat to make a round trip, we need to consider the time taken for both the downstream and upstream displacements separately, and then add them together.
For the downstream displacement:
Speed of boat relative to water = speed of boat + speed of water
= 5 m/s + 1.3 m/s
= 6.3 m/s
Distance downstream = 215 m
Time taken = Distance / Speed
= 215 m / 6.3 m/s
= 34.127 seconds
For the upstream displacement:
Speed of boat relative to water = speed of boat - speed of water
= 5 m/s - 1.3 m/s
= 3.7 m/s
Distance upstream = 215 m
Time taken = Distance / Speed
= 215 m / 3.7 m/s
= 58.108 seconds
To find the total time for the round trip, add the times for the downstream and upstream displacements:
Total time = Time downstream + Time upstream
= 34.127 seconds + 58.108 seconds
= 92.235 seconds
Therefore, it takes approximately 92.235 seconds for the boat to make the round trip consisting of a 215 m displacement downstream followed by a 215 m displacement upstream.