A swimmer is capable of swimming 0.45 m/s in still water.
(a) If she aims her body directly across a 75 m-wide river whose current is 0.30 m/s, how far downstream (from a point opposite her starting point) will she land?
(b) How long will it take her to reach the other side?
just need answer, i did all the work and want the right answer to check it with. Thanks <3
If you show your work, I will be glad to help.
To find the answers to these questions, we need to use some basic concepts of relative motion.
(a) To determine how far downstream the swimmer will land, we need to calculate the component of the river's current perpendicular to her original direction of motion.
The swimmer's velocity relative to the water can be calculated using vector addition. We subtract the velocity of the river's current from the swimmer's speed in still water:
Relative velocity = (0.45 m/s) - (0.30 m/s) = 0.15 m/s
The time it takes the swimmer to cross the river can be found by dividing the width of the river by the relative velocity:
Time = (Width of the river) / (Relative velocity)
Time = 75 m / 0.15 m/s
Time = 500 seconds
Finally, to find how far downstream the swimmer will land, we multiply the time by the velocity of the river's current:
Distance downstream = (Time) * (Current velocity)
Distance downstream = (500 s) * (0.30 m/s)
Distance downstream = 150 m
Therefore, the swimmer will land 150 meters downstream (from a point opposite her starting point).
(b) To find how long it will take the swimmer to reach the other side, we need to calculate the total time taken, considering both the time to cross the river and the time needed to counteract the downstream drift caused by the current.
The time to cross the river is already calculated as 500 seconds.
The downstream drift caused by the current is calculated by multiplying the current velocity by the total time taken:
Downstream drift = (Current velocity) * (Total time)
Downstream drift = (0.30 m/s) * (500 s)
Downstream drift = 150 m
To find the total time, we need to consider the swimmer's speed in still water and the upstream velocity required to counteract the downstream drift.
The upstream velocity is calculated as:
Upstream velocity = (Downstream drift) / (Total time)
Upstream velocity = 150 m / 500 s
Upstream velocity = 0.30 m/s
Now, the swimmer's velocity relative to the water in the upstream direction can be calculated using vector addition:
Relative velocity = (Swimmer's speed in still water) + (Upstream velocity)
Relative velocity = 0.45 m/s + 0.30 m/s
Relative velocity = 0.75 m/s
The total time taken to cross the river can be found using the width of the river and the relative velocity as before:
Total time = (Width of the river) / (Relative velocity)
Total time = 75 m / 0.75 m/s
Total time = 100 seconds
Therefore, it will take the swimmer 100 seconds to reach the other side.