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Kayaker paddling across a harbor

  • Thread starter magic-400
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  • #1
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Homework Statement



A kayaker needs to paddle north across a 105 m wide harbor. The tide is going out, creating a tidal current that flows to the east at 1.5 m/s. The kayaker can paddle with a speed of 3.4 m/s.

(a) In which direction should he paddle in order to travel straight across the harbor? (degrees west of north)

(b) How long will it take him to cross? (seconds)

Homework Equations



c^2= a^2 + b^2

The Attempt at a Solution



I divided 105m by 3.4 m/s to determine how long it would take to go straight across the harbor. Then I multiplied that number (30.88) by 1.5 m/s to get the distance he would have ended up downstream. 46.32m.

Then, I attempted to set up a right triangle and solve for the angle but that's where I got confused.
 

Answers and Replies

  • #2
PeterO
Homework Helper
2,425
46

Homework Statement



A kayaker needs to paddle north across a 105 m wide harbor. The tide is going out, creating a tidal current that flows to the east at 1.5 m/s. The kayaker can paddle with a speed of 3.4 m/s.

(a) In which direction should he paddle in order to travel straight across the harbor? (degrees west of north)

(b) How long will it take him to cross? (seconds)

Homework Equations



c^2= a^2 + b^2

The Attempt at a Solution



I divided 105m by 3.4 m/s to determine how long it would take to go straight across the harbor. Then I multiplied that number (30.88) by 1.5 m/s to get the distance he would have ended up downstream. 46.32m.

Then, I attempted to set up a right triangle and solve for the angle but that's where I got confused.
The kayaker will take longer than [30.88] that to cross the harbour, since he/she is not paddling directly towards the opposite side.
 
  • #3
1,065
10
1. Homework Statement

A kayaker needs to paddle north across a 105 m wide harbor. The tide is going out, creating a tidal current that flows to the east at 1.5 m/s. The kayaker can paddle with a speed of 3.4 m/s.

(a) In which direction should he paddle in order to travel straight across the harbor? (degrees west of north)

(b) How long will it take him to cross? (seconds)

Then, I attempted to set up a right triangle and solve for the angle but that's where I got confused.

-----------------------------------------------------
Yes you can use a right triangle to solve the problem.
This is a vector problem and using a right triangle geometry is one of the methods.

Kayaker speed with direction is one vector.
The tide speed and direction is another vector.
You can do operations on this 2 vectors and in this example adding the two vectors.

The sum of the two vectors will result in the kayaker paddling straight across the habour.
 
  • #4
CWatters
Science Advisor
Homework Helper
Gold Member
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What azizlwl said.

If still stuck post your attempt at the vector diagram.
 

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