Answer:
To solve this problem, we need to use some principles of physics, specifically Newton's second law (F=ma) and the equations of motion. Here are the steps:
1. Calculate the acceleration (a)
We can use the equation of motion to find the acceleration:
v_f^2 = v_i^2 + 2a*d
where:
v_f = final velocity = 6.80 m/s
v_i = initial velocity = 3.00 m/s
d = distance = 2/3 of the length of the fish = 2/3 * 1.50 m = 1.00 m
a = acceleration (which we are trying to find)
Rearranging the equation to solve for a gives us:
a = (v_f^2 - v_i^2) / (2*d)
2. Calculate the magnitude of the force F
Once we have the acceleration, we can use Newton's second law (F=ma) to calculate the force. The net force acting on the fish as it jumps out of the water is the difference between the upward force F exerted by the tail fin and the downward force due to gravity (mg). The net force is also equal to the product of the mass of the fish and its acceleration (ma). Therefore, we have:
F - mg = ma
Rearranging this equation to solve for F gives us:
F = ma + mg
Now let's plug in the numbers and do the calculations.
First, let's find the acceleration:
a = (v_f^2 - v_i^2) / (2*d)
a = (6.80 m/s)^2 - (3.00 m/s)^2) / (2*1.00 m)
a = (46.24 m^2/s^2 - 9.00 m^2/s^2) / 2 m
a = 37.24 m^2/s^2 / 2 m
a = 18.62 m/s^2
The salmon's acceleration is 18.62 m/s^2 upward.
Next, let's find the force F. We know the mass of the fish is 52.0 kg, and the acceleration due to gravity is approximately 9.8 m/s^2. So,
F = ma + mg
F = (52.0 kg)(18.62 m/s^2) + (52.0 kg)(9.8 m/s^2)
F = 969.24 N + 509.6 N
F = 1478.84 N
So, the magnitude of the force F exerted by the salmon's tail fin during this interval is approximately 1479 N.