How High Can a Salmon Jump Using Its Maximum Speed?

[Touchme]

salmon motion problem

Hi,

A Chinook Salmon has a maximum underwater speed of 3.58 m/s, but it can jump out of water with a speed of 6.68 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 1.40 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.)

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?

I tried using 6.68 as initial velocity, determine the time when it reaches max height (final velocity = 0). I use the time, initial velocity, and 9.8 to solve for the max height. The answer i got was 2.2766 m and its wrong. Can someone help me with this problem. Thank you

 

[andrevdh]

The waterfall is parabolic motion of "pieces" of water. I assume that a piece of water leaves the ledge horizontally with a speed of 1.40 m/s. As this piece of water travels along a parbolic path its speed increases. You need to calculate the vertical distance below the ledge where such a piece of water reaches a speed of 3.00 m/s. The salmon need to be able to jump up to this point in order to swim the remaining distance up to the ledge. Note that the answer asks the height of the ledge above the point where the salmon leaves the stream while jumping up to this point in the waterfall. So the answer is the sum of these two distances - jumping height and distance below ledge.

 

[Touchme]

Thank you for clarifying what the question is asking for and thanks for the tip.

 

[andrevdh]

Remember that the speed of a projectile is determined by its both its velocity components.

 

[parwana]

so how do u do part b- 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?? I can't get it right

 

[andrevdh]

What have you been able to determine thus far?

The maximum jumping height? What do you get for this distance?

The distance below the ledge where the water reaches a speed of 3.00 m/s?

 

[parwana]

I got the distance below the ledge= .3 m

 

[parwana]

help please for part b

 

[andrevdh]

The values are to three significant digits in the problem. So please give your answers to the same. I get a slightly different value for the below the ledge distance. How did you get to your answer?

Do you have a problem in calculating the maximum jumping height of the salmon? To reach the point where the water speed is 3.00 m/s he will launch himself out of the water with a speed of 6.68 m/s and his speed at the top of his jump will be zero. What is his jumping height then?