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

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Geometric vectors can be applied to solve the river crossing problem by analyzing the boat's motion relative to the current. The boat, traveling at 20 km/h perpendicular to the river's flow, will drift downstream due to the river's current of 6 km/h. The resultant distance downstream from the marina is calculated to be 0.6 km, with the crossing taking 6 minutes. The discussion emphasizes the importance of understanding the components of motion rather than solely focusing on resultant velocity. Ultimately, the problem illustrates how vector analysis can effectively determine the boat's trajectory and crossing time.
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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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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 ?
 
Sorry, but how do you compute all three sides when you only have the perpendicular distance of 2km?
 
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:
 

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