A Chinook salmon can swim underwater at 3.75 m/s, and it can also jump vertically upward, leaving the water with a speed of 6.20 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.

P = 2161 N

Explanation:

For this exercise, let's start with Newton's second law

                P - W = m a

                P = ma + W

Where P is the fin force, W the weight,

Let's look for the vertical acceleration of the fish, this goes from a vertical speed of zero to a speed of 6.20 m / s when it has traveled half its length 1.50

                  y = 0.75 m

                  v² = v₀ + 2 a y

                  a = v² / 2 y

                  a = 6.20²/2 0.75

                  a = 25.63 m / s

We substitute in Newton's second law

                  P = m (g + a)

Let's calculate

                 P = 61.0 (0 9.8 + 25.63)

                P = 2161 N

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.