Question

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?

Answer 1

v_c = 0.7 m / s east

Step-by-step 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