As a fish jumps vertically out of the water, assume that only two significant forces act on it: an upward force F exerted by the tail fin and the downward force due to gravity. A record Chinook salmon has a length of 1.50 m and a mass of 49.5 kg. If this fish is moving upward at 3.00 m/s as its head first breaks the surface and has an upward speed of 5.60 m/s after two-thirds of its length has left the surface, assume constant acceleration and determine the following.

(a) the salmon's acceleration?
(b) the magnitude of the force F during this interval?

I know for the second part i have to do F(Total) = m( a + g). But i don't know how to solve for the accelaration

the average speed over the interval is (3.00 m/s + 5.60 m/s) / 2 = 4.30 m/s

2/3 of its length is 1.00 m

so the time of the interval is
... 1.00 m / 4.30 m/s

the change in speed is
... 5.30 m/s - 3.00 m/s

acceleration is ... speed change / time

Okay so I solved for it then plugged my answer (11.3) into the second equation and got 1044. Thank you!

To solve this problem, we will use the principles of motion and forces. Let's break it down into two parts:

Part 1: Finding the acceleration
We are given that the fish is moving upward with an initial velocity (u) of 3.00 m/s as its head first breaks the surface and a final velocity (v) of 5.60 m/s when two-thirds of its length has left the surface. We need to find the acceleration (a) of the fish.

We can use the equation of motion:

v^2 = u^2 + 2aS

Where:
v = final velocity
u = initial velocity
a = acceleration
S = displacement

In this case, the displacement (S) is equal to two-thirds of the fish's length, or (2/3) * 1.50 m.

Plugging in the values:

(5.60 m/s)^2 = (3.00 m/s)^2 + 2a * (2/3) * 1.50 m

Simplifying the equation:

31.36 - 9 = (4/3) * a * 1.50

22.36 = (4/3) * a * 1.50

Now, isolate the acceleration (a) by dividing both sides by [(4/3) * 1.50]:

a = 22.36 / [(4/3) * 1.50]

Calculate the value to find the acceleration.

Part 2: Finding the magnitude of the force F
To find the magnitude of the force F, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration:

F = m * a

We are given the mass of the fish, which is 49.5 kg, and we have already calculated the acceleration in Part 1.

Plug in the values to calculate the magnitude of the force F.

Solve for F.

(a) Acceleration: Calculate the value obtained in Part 1.
(b) Magnitude of the force F: Calculate the value obtained in Part 2.