A Chinook salmon can swim underwater at 3.35 m/s, and it can also jump verticall

Question

A Chinook salmon can swim underwater at 3.35 m/s, and it can also jump vertically upward, leaving the water with a speed of 6.19 m/s. A record salmon has length 1.50 m and mass 61.0 kg. Consider the fish swimming straight upward in the water below the surface of a lake. The gravitational force exerted on it is very nearly canceled out by a buoyant force exerted by the water. The fish experiences an upward force P exerted by the water on its threshing tail fin and a downward fluid friction force that we model as acting on its front end. Assume the fluid friction force disappears as soon as the fish's head breaks the water surface and assume the force on its tail is constant. Model the gravitational force as suddenly switching full on when half the length of the fish is out of the water. Find the value of P.
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Explanation / Answer

Consider the velocity components of the salmon and the river. For the salmon, it is moving at v1 = 0 horizontally (in x), but the river is moving at v2 = 1.50m/s in x. This works out to an actual speed for the salmon of (horizontally): v(x) = v1- v2 = 0 - 1.50m/s = -1.50m/s Here, the salmon has vertical speed of v1=5.79m/s, but the river has no vertical speed, so for the salmon's speed vertically: v(y) = 5.79m/s - 0 = 5.79m/s The salmon's actual (vector) speed then is: v² = v(x)² + v(y)² = -(1.50m/s)² + (5.79m/s)² v = 5.59m/s Then, the height it achieves above the water is: v² = v0² + 2g?y ?y = (v² - v0²) / 2g = [0 - (5.59m/s)²] / (2 x -9.80m/s²) = 1.59m Hope this helps.

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