Simple boat and river question(Vectors)

[dmitrip]

Homework Statement

In his rowboat, Pierre heads directly across a river at a speed of 10 km/h. The river is 120m wide and is flowing at 6 km/h.

Suppose Pierre wants to row directly across the river. At what angle relative to the shore should he head?

I would really appreciate help with this question, since I know that it is suppose to be straight forward and for some reason I just can't solve it! must be because I didn't have much of a sleep.

thanks alot

 

[AFG34]

Vbg = Vbw + Vwg
where Vbg is the velocity of the boat relative to the ground, Vbw is the velocity of boat relative to water, Vwg is the veloctiy of the water relative to the ground.

 

[Moetasim]

To solve this problem, we need to use vector addition to determine the direction that Pierre should row in. The velocity of the river can be represented by a vector pointing to the right with a magnitude of 6 km/h. The velocity of the boat can be represented by a vector pointing directly across the river with a magnitude of 10 km/h.

To find the angle between these two vectors, we can use the tangent function. The formula for tangent is opposite/adjacent, which in this case would be the y-component of the velocity of the boat (10 km/h) divided by the x-component of the velocity of the river (6 km/h).

Therefore, the angle that Pierre should row at can be calculated as arctan(10/6) = 59.04 degrees. This means that he should row at an angle of approximately 59 degrees relative to the shore.

I hope this helps you solve the problem. It is important to get enough rest before attempting difficult problems, as a well-rested mind can think more clearly and effectively. Keep practicing and you will get better at solving these types of questions. Good luck!