A family decided to take a canoe trip one summer. After paddling for an hour, they decided to drift along with the river current to take a break. When they stop, the canoe is traveling east at 1.3 m/s while the river current is moving 0.2 m/s to the west. When the canoe drifts into the path of another river that joins the first, the west-moving current is 0.8 m/s. How will the canoe be affected?

 v_c = 0.7 m / s    east

Explanation:

This is a one-dimensional velocity addition problem.

1 part

The canoe goes to v_ = 1.3 m / s towards the east and the river goes to

v_r = 0.2 m / s towards the west, if we assume that the direction towards the east is positive v_r = -0.2 m / s

the speed of the canoe with respect to the land is the speed of the canoe with respect to the river plus the speed of the river with respect to the land

             v_c = v_{cr} + v_r

             v_{cr} = v_c - v_r

             v_{cr} = 1.3 - (-0.2)

             v_{cr} = 1.5 m / s

this is the speed of the with respect to the river.

2 part

now we enter a river that the speed is v_r = -0.8 m / s, therefore the speed of the canoe with respect to the land is

              v_c = v_{cr} + v_r

              v_c = 1.5 - 0.8

              v_c = 0.7 m / s

the positive sign indicates that it continues to move east

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.