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Kayaker paddling across a harbor

by magic-400
Tags: angle, degree, direction, triangle, vector
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magic-400
#1
Sep14-12, 03:39 PM
P: 1
1. The problem statement, all variables and given/known data

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)

2. Relevant equations

c^2= a^2 + b^2

3. 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.
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PeterO
#2
Sep14-12, 07:29 PM
HW Helper
P: 2,318
Quote Quote by magic-400 View Post
1. The problem statement, all variables and given/known data

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)

2. Relevant equations

c^2= a^2 + b^2

3. 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.
azizlwl
#3
Sep14-12, 07:55 PM
P: 963
1. The problem statement, all variables and given/known data

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.

CWatters
#4
Sep15-12, 04:20 AM
P: 3,268
Kayaker paddling across a harbor

What azizlwl said.

If still stuck post your attempt at the vector diagram.


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