How can geometric vectors be used to solve a river crossing problem?

In summary, a river that is 2 km wide and flows at 6 km/h is being crossed by a motor boat with a speed of 20 km/h in still water. Using geometric vectors, the boat will reach the opposite bank 0.6 km downstream from the marina and it will take 6 minutes to do so. The distance and time are found by computing the sides of a triangle with lengths 2 km, 0.6 km, and 2.08 km. The question does not require finding the resultant velocity.
  • #1
a.a
127
0

Homework Statement


1. Homework Statement

A river is 2 km wide and flows at 6 km/h. A motor boat that has a speed of
20 km/h in still water heads out from one bank perpendicular to the current.
A marina lies directly across the river on the opposite bank. Use Geometric
Vectors to solve this problem.

a. How far downstream from the marina will the boat reach the other bank? (Answer: 0.6 km)
b. How long will it take? (Answer: 6 min)



Homework Equations



sine and cosine reltions

The Attempt at a Solution



I've found that the resultant velocity of the boat would be 20.88 km/h, but I am not sure how to find the distance (horizontal) that the boat travells.
 
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  • #2
a.a said:

Homework Statement



I've found that the resultant velocity of the boat would be 20.88 km/h, but I am not sure how to find the distance (horizontal) that the boat travells.

It's a triangle. Compute all the sides.

2 km, .6 km, 2.08 km

BTW, what makes you think the velocity of the perpendicular boat isn't 20km/h ?
 
  • #3
Sorry, but how do you compute all three sides when you only have the perpendicular distance of 2km?
 
  • #4
a.a said:
I've found that the resultant velocity of the boat would be 20.88 km/h, but I am not sure how to find the distance (horizontal) that the boat travells.

Hi a.a! :smile:

The question does not ask you for the resultant velocity, and you don't need to find it to answer the question.

Think again. :smile:
 

What is the cosine vector equation?

The cosine vector equation is a mathematical formula that represents the relationship between two vectors in a given space. It is used to calculate the cosine of the angle between two vectors.

How is the cosine vector equation calculated?

The cosine vector equation is calculated by taking the dot product of two vectors and dividing it by the product of their magnitudes. This can also be represented as the cosine of the angle between the two vectors.

What is the significance of the cosine vector equation?

The cosine vector equation is significant because it allows us to determine the relationship between two vectors in a given space. It is commonly used in physics and engineering to calculate forces and angles between objects.

Can the cosine vector equation be used for any type of vector?

Yes, the cosine vector equation can be used for any type of vector, including 2D and 3D vectors. It is a universal equation that can be applied to any vector in a given space.

Are there any limitations to using the cosine vector equation?

The cosine vector equation is limited to calculating the relationship between two vectors in a given space. It cannot be used for vectors in different spaces or for non-vector quantities.

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