Question

A kayaker needs to paddle north across a 100 -m wideharbor. The tide is going out, creating a tidal current that flowsto the east at 2.0 m/s. The Kayaker can paddle with a speed of3.0m/s.
a. In which direction shoule he paddle in order to travel straightacross the harbor ?
b. How long will it take him to cross ?  

   A body diagram and step by step precise solution willgive me a better understanding .. thanks for you help..   

Answer 1

Concepts and reason

Determine the direction in which Kayaker should paddle in order to travel straight across the harbour by using trigonometry concept. Next calculate, speed by using Pythagoras theorem, then find time by using relation between speed and time.

Fundamentals

A right angle triangle is defined as in which one angle is right angle and the side opposite to the right angle is called as the hypotenuse which is the longest side of the right angle triangle.

In any right angle triangle as shown below:

The angle can be determined if the perpendicular and hypotenuse are known as:

And the Pythagoras theorem can be applied as:

The speed time formula is as:

(a)

The Kayaker need to paddle north across a wideharbor with a speed of .But the tide is going out, creating a tidal current that flows to the east at. This information can be represented in diagram form as:

To determine the direction in which Kayaker should paddle in order to travel straight across the harbour you have to determine the angle.

Since in this right angle triangle the perpendicular and hypotenuse are known therefore:

(b)

Since The Kayaker need to paddle north across a wideharbor with a speed of .But the tide is going out, creating a tidal current that flows to the east at. This information can be represented in diagram form as:

From the Pythagoras theorem the resultant speed is as:

From the speed time formula the time required to cross the harbour is as:

Therefore, substitute the distance of the harbour and the resultant speed

Ans: Part a

The kayaker should paddle towards North West to travel straight across the harbour.

Part b

The time required to cross the harbour is.