Complete Question:
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 48.0 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 6.30 m/s after two-thirds of its length has left the surface, assume constant acceleration and determine the following. (a) the salmon's acceleration m/s2 upward (b) the magnitude of the force F during this interval N
Answer:
(a) acceleration = 15.3 ms⁻²
(b) Magnitude of net force = 734.4 N
Magnitude of upward force exerted by tail fin = 1204.8 N
Explanation:
Mass of the salmon fish = 48 kg
Length of the Salmon Fish = 1.5 m
g = 9.8 ms⁻²
(a) salmon's acceleration during the time interval N:
Downward Force on the fish is equal to the Force due to gravity and is given as:
F₂ = mg
= 48 * 9.8
= 470.4 N
The direction of movement of the fish is upward and the acceleration is constant. We are given two different velocities of fish at two different instances.
- When the head breaks out of the water surface first:
Initial velocity = v₁ = 3 m/s
- When two third of its body length is out = d = 1 m
Final Velocity = v₂ = 6.3 m/s
Using the third equation of motion:
2*a*d = v₂² - v₁²
a = (6.3² - 3²)/2*1
a = 15.3 ms⁻²
(b) magnitude of force F during this interval N = ?
We are assuming that F is the net force consisting of both the upward and the downward force.
According to Newton's 2nd law of motion, Force is given as:
F = ma
F = 48 kg * 15.3
F = 734.4 N
Magnitude of upward Force = Fₓ
Force Fₓ exerted by the tail fin of the fish is given by
F = Fₓ - F₂
That is the net force is the sum of the upward and downward forces acting on the fish body. Fₓ is positive because it is in upward direction and F₂ is negative because it is in downward direction. F which is the net force here is positive as Fₓ > F₂.
=> Fₓ = F + F₂
Fₓ = 734.4 + 470.4
Fₓ = 1204.8 N
