Magnitude and Direction, Canoe on River

[ap_physics]

Homework Statement

A canoe has a velocity of 0.35 m/s southwest relative to the earth. The canoe is on a river that is flowing 0.65 m/s east relative to the earth. Find the velocity (magnitude and direction) of the canoe relative to the river.

The Attempt at a Solution

0.930985 is the magnitude.
Then I have no clue how to get the angle in terms of counterclockwise from east.

Thanks very much in advance!

 

[gneill]

Homework Statement

A canoe has a velocity of 0.35 m/s southwest relative to the earth. The canoe is on a river that is flowing 0.65 m/s east relative to the earth. Find the velocity (magnitude and direction) of the canoe relative to the river.

The Attempt at a Solution

0.930985 is the magnitude.
Then I have no clue how to get the angle in terms of counterclockwise from east.

Thanks very much in advance!

Hi ap_physics; Welcome to Physics Forums.

How did you arrive at an angle of 315 degrees for the canoe's velocity? I would have thought that "southwest" would be halfway between south and west.

Edit: I see you've edited your original so that the angles of the vectors are no longer shown. Perhaps you could just explain your approach to the problem?

 

[ap_physics]

Well, I posted my attempt earlier, but it was wrong, and I was given the answer for the velocity by my teacher, as it was too complicated for our level. But, he says I can still find the angle. But, I don't know which formula to use.

 

[gneill]

Well, I posted my attempt earlier, but it was wrong, and I was given the answer for the velocity by my teacher, as it was too complicated for our level. But, he says I can still find the angle. But, I don't know which formula to use.

Okay, what have you learned so far about adding and subtracting vectors? Have you learned how to determine their angles from their x and y components?

 

[Nickie]

I would first clarify the given information. The statement mentions that the canoe has a velocity of 0.35 m/s southwest relative to the earth. This means that the canoe is moving at a speed of 0.35 m/s in a direction that is 45 degrees southwest from the east-west axis.

Next, the statement mentions that the river is flowing at a velocity of 0.65 m/s east relative to the earth. This means that the river is moving at a speed of 0.65 m/s in the direction of due east.

To find the velocity of the canoe relative to the river, we can use vector addition. This means that we need to add the velocities of the canoe and the river to get the resultant velocity.

Using the Pythagorean theorem, we can calculate the magnitude of the resultant velocity as follows:

Resultant velocity = √(0.35^2 + 0.65^2) = 0.75 m/s

To find the direction of the resultant velocity, we can use trigonometry. The angle between the resultant velocity and the east-west axis can be found using the inverse tangent function as follows:

Angle = tan^-1 (0.65/0.35) = 61.63 degrees

Since the canoe is moving towards the southwest, the angle between the resultant velocity and the east-west axis would be 180 - 61.63 = 118.37 degrees.

Therefore, the velocity of the canoe relative to the river is 0.75 m/s at an angle of 118.37 degrees counterclockwise from due east.