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.)

Question

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?

Do this problem in two steps.

<< 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?>>

Use conservation of energy to get he distance Y1 that the water must fall to have a velocity of 3.00 m/s.
M g Y1 = (1/2) M [(3 m/s)^2 - (1.4 m/s)^2]
The mass M cancels out. Solve for Y1.

<<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?
>>
Use conservation of energy again. The distance Y2 that the salmon can rise is
given by
M g Y2 = (1/2) M (6.58)^2
The unknown M (of the salmon) once again cancels out. Solve for Y2

Y1 + Y2 is the maximum waterfall height that can be climbed by swimming from Y2 to the top (rising out of the water a distance Y1, re-entering the water and swimming Y2 to the top).

Answer 1

2.45