# Kayaker paddling across a harbor

## 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)

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

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PeterO
Homework Helper

## 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)

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.

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.

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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
Homework Helper
Gold Member
What azizlwl said.

If still stuck post your attempt at the vector diagram.