Optimizing Salmon's Upstream Movement: Understanding Speed and Height Limits

[parwana]

A Chinook Salmon has a maximum underwater speed of 3.58 m/s, but it can jump out of water with a speed of 6.56 m/s. to move upstream past a waterfall, the salmon does not need to jump to the top of the fall, but only to a point in the fall where the water speed is less than 3.58 m/s; it can then swim up the fall for the remaining distance. Because the salmon must make forward progress in the water, let's assume that it can swim to the top if the water speed is 3.00 m/s. If water has a speed of 1.75 m/s as it passes over a ledge, how far below the ledge will the water be moving with a speed of 3.00 m/s? (Note that water undergoes projectile motion once it leaves the ledge.)

m below the ledge?

If the salmon is able to jump vertically upward from the base of the fall, what is the maximum height of waterfall that the salmon can clear?
m?

 

[andrevdh]

This question have been asked in this post

https://www.physicsforums.com/showthread.php?t=133331"

a while ago.

 

[kyle8921]

I would approach this question by first understanding the physical capabilities and limitations of the Chinook Salmon. Based on the information provided, we know that the salmon has a maximum underwater speed of 3.58 m/s and a jumping speed of 6.56 m/s. From this, we can infer that the salmon has a strong ability to propel itself through water, but also has the agility and strength to jump out of the water at high speeds.

In order to optimize the salmon's upstream movement, we need to understand the relationship between water speed and the salmon's ability to swim and jump. From the given information, we can calculate that in order for the salmon to successfully swim up the fall, the water speed must be less than 3.58 m/s. Therefore, if the water speed is 1.75 m/s, the salmon would be able to swim up the fall for the remaining distance.

However, we must also consider the salmon's ability to jump vertically from the base of the fall. In order to clear a waterfall, the salmon would need to jump to a height that is greater than the height of the waterfall. Using the given information, we can calculate that the maximum height of a waterfall that the salmon can clear is approximately 1.84 m. This is calculated by taking the jumping speed of 6.56 m/s and dividing it by the gravitational acceleration of 9.8 m/s^2.

In summary, understanding the speed and height limits of the Chinook Salmon is crucial in optimizing its upstream movement. By considering the salmon's swimming and jumping abilities, we can determine the maximum water speed it can swim against and the maximum height of a waterfall it can clear. This information can be used to inform conservation efforts and ensure the survival of this important species.