A Chinook salmon has a maximum underwater speed of 3.0 m/s, and can jump out of the water vertically with a speed of 4.8 m/s. A record salmon has a length of 1.5 m and a mass of 62 kg. When swimming upward at constant speed, and neglecting buoyancy, the fish experiences three forces: an upward force F exerted by the tail fin, the downward drag force of the water, and the downward force of gravity. As the fish leaves the surface of the water, however, it experiences a net upward force causing it to accelerate from 3.0 m/s to 4.8 m/s. Assuming the drag force disappears as soon as the head of the fish breaks the surface and that F is exerted until two-thirds of the fish's length has left the water, determine the magnitude of F.

Question

A Chinook salmon has a maximum underwater speed of 3.0 m/s, and can jump out of the water vertically with a speed of 4.8 m/s. A record salmon has a length of 1.5 m and a mass of 62 kg. When swimming upward at constant speed, and neglecting buoyancy, the fish experiences three forces: an upward force F exerted by the tail fin, the downward drag force of the water, and the downward force of gravity. As the fish leaves the surface of the water, however, it experiences a net upward force causing it to accelerate from 3.0 m/s to 4.8 m/s. Assuming the drag force disappears as soon as the head of the fish breaks the surface and that F is exerted until two-thirds of the fish's length has left the water, determine the magnitude of F.

Answer 1

To determine the magnitude of the upward force F exerted by the fish's tail fin, we need to analyze the forces acting on the fish. Let's break down the problem step by step.

Step 1: Calculate the acceleration of the fish from 3.0 m/s to 4.8 m/s.
The change in velocity (𝑣) is 𝑣 = 4.8 m/s - 3.0 m/s = 1.8 m/s.
The time taken (𝑡) for this acceleration is not given, so we cannot calculate the acceleration directly from 𝑎 = (𝑣-𝑢)/𝑡. We will need additional information or assumptions for this step.

Step 2: Calculate the drag force experienced by the fish.
Since the drag force disappears as soon as the head of the fish breaks the surface, we only need to consider the drag force for two-thirds (2/3) of the fish's length.

The drag force (𝐹𝐷) acting on a moving object in a fluid is given by the equation 𝐹𝐷 = 0.5 × 𝐶𝐷 × 𝜌 × 𝐴 × 𝑣^2, where 𝐶𝐷 is the drag coefficient, 𝜌 is the density of water, 𝐴 is the cross-sectional area, and 𝑣 is the velocity of the object.

To calculate the drag force, we need to know the drag coefficient (𝐶𝐷), the density of water (𝜌), the cross-sectional area (𝐴), and the velocity of the fish (𝑣). Unfortunately, none of these values are provided in the question. We will need additional information or assumptions for this step.

Step 3: Calculate the net upward force acting on the fish.
When the fish leaves the surface of the water, it accelerates from 3.0 m/s to 4.8 m/s. This acceleration is caused by a net upward force (𝐹𝑛𝑒𝑡).

The net force (𝐹𝑛𝑒𝑡) is given by the equation 𝐹𝑛𝑒𝑡 = 𝑚 × 𝑎, where 𝑚 is the mass of the fish, and 𝑎 is the acceleration.

We know the mass of the fish (62 kg), but the acceleration is not directly provided. We need additional information or assumptions to calculate the net upwards force.

Step 4: Determine the magnitude of the upward force F.
To find the magnitude of the upward force F exerted by the fish's tail fin, we need to analyze the forces when swimming upward at constant speed (prior to leaving the surface of the water). Unfortunately, the question does not provide any information or assumptions about F.

Since we are unable to obtain the necessary information or make reasonable assumptions, we cannot determine the magnitude of the upward force exerted by the fish's tail fin (F).